Triunghi - Wikipedia

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class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Definiții</span> </div> </a> <ul id="toc-Definiții-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Clasificare" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Clasificare"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Clasificare</span> </div> </a> <button aria-controls="toc-Clasificare-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Clasificare subsection</span> </button> <ul id="toc-Clasificare-sublist" class="vector-toc-list"> <li id="toc-În_funcție_de_lungimile_laturilor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#În_funcție_de_lungimile_laturilor"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>În funcție de lungimile laturilor</span> </div> </a> <ul id="toc-În_funcție_de_lungimile_laturilor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-După_felul_unghiurilor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#După_felul_unghiurilor"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>După felul unghiurilor</span> </div> </a> <ul id="toc-După_felul_unghiurilor-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Drepte,_segmente_și_puncte_remarcabile" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Drepte,_segmente_și_puncte_remarcabile"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Drepte, segmente și puncte remarcabile</span> </div> </a> <button aria-controls="toc-Drepte,_segmente_și_puncte_remarcabile-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Drepte, segmente și puncte remarcabile subsection</span> </button> <ul id="toc-Drepte,_segmente_și_puncte_remarcabile-sublist" class="vector-toc-list"> <li id="toc-Bisectoarea" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bisectoarea"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Bisectoarea</span> </div> </a> <ul id="toc-Bisectoarea-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Înălțimea" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Înălțimea"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Înălțimea</span> </div> </a> <ul id="toc-Înălțimea-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mediana" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mediana"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Mediana</span> </div> </a> <ul id="toc-Mediana-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mediatoarea" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mediatoarea"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Mediatoarea</span> </div> </a> <ul id="toc-Mediatoarea-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Linia_mijlocie" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Linia_mijlocie"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Linia mijlocie</span> </div> </a> <ul id="toc-Linia_mijlocie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Centrul_cercului_circumscris" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Centrul_cercului_circumscris"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>Centrul cercului circumscris</span> </div> </a> <ul id="toc-Centrul_cercului_circumscris-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Centrul_cercului_înscris" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Centrul_cercului_înscris"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.7</span> <span>Centrul cercului înscris</span> </div> </a> <ul id="toc-Centrul_cercului_înscris-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ortocentrul" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ortocentrul"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.8</span> <span>Ortocentrul</span> </div> </a> <ul id="toc-Ortocentrul-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Centrul_de_greutate" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Centrul_de_greutate"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.9</span> <span>Centrul de greutate</span> </div> </a> <ul id="toc-Centrul_de_greutate-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Congruență" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Congruență"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Congruență</span> </div> </a> <button aria-controls="toc-Congruență-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Congruență subsection</span> </button> <ul id="toc-Congruență-sublist" class="vector-toc-list"> <li id="toc-Criterii_de_congruență" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Criterii_de_congruență"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Criterii de congruență</span> </div> </a> <ul id="toc-Criterii_de_congruență-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Congruența_triunghiurilor_dreptunghice" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Congruența_triunghiurilor_dreptunghice"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Congruența triunghiurilor dreptunghice</span> </div> </a> <ul id="toc-Congruența_triunghiurilor_dreptunghice-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Asemănare" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Asemănare"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Asemănare</span> </div> </a> <button aria-controls="toc-Asemănare-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Asemănare subsection</span> </button> <ul id="toc-Asemănare-sublist" class="vector-toc-list"> <li id="toc-Criterii_de_asemănare" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Criterii_de_asemănare"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Criterii de asemănare</span> </div> </a> <ul id="toc-Criterii_de_asemănare-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Teoreme_și_consecințe" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Teoreme_și_consecințe"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Teoreme și consecințe</span> </div> </a> <ul id="toc-Teoreme_și_consecințe-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Reguli,_proprietăți,_teoreme_aplicabile" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Reguli,_proprietăți,_teoreme_aplicabile"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Reguli, proprietăți, teoreme aplicabile</span> </div> </a> <ul id="toc-Reguli,_proprietăți,_teoreme_aplicabile-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Formule" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Formule"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Formule</span> </div> </a> <button aria-controls="toc-Formule-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Formule subsection</span> </button> <ul id="toc-Formule-sublist" class="vector-toc-list"> <li id="toc-Perimetru_și_semiperimetru" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Perimetru_și_semiperimetru"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Perimetru și semiperimetru</span> </div> </a> <ul id="toc-Perimetru_și_semiperimetru-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Arie" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Arie"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Arie</span> </div> </a> <ul id="toc-Arie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Alte_formule" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Alte_formule"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3</span> <span>Alte formule</span> </div> </a> <ul id="toc-Alte_formule-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Note" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Note"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Note</span> </div> </a> <ul id="toc-Note-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografie" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Bibliografie"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Bibliografie</span> </div> </a> <ul id="toc-Bibliografie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lectură_suplimentară" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Lectură_suplimentară"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Lectură suplimentară</span> </div> </a> <ul id="toc-Lectură_suplimentară-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Legături_externe" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Legături_externe"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Legături externe</span> </div> </a> <ul id="toc-Legături_externe-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Cuprins" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Comută cuprinsul" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Comută cuprinsul</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Triunghi</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Mergeți la un articol în altă limbă. Disponibil în 162 limbi" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-162" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">162 limbi</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ab mw-list-item"><a href="https://ab.wikipedia.org/wiki/%D0%90%D1%85%D0%BA%D3%99%D0%B0%D0%BA%D1%8C" title="Ахкәакь – abhază" lang="ab" hreflang="ab" data-title="Ахкәакь" data-language-autonym="Аԥсшәа" data-language-local-name="abhază" class="interlanguage-link-target"><span>Аԥсшәа</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Driehoek" title="Driehoek – afrikaans" lang="af" hreflang="af" data-title="Driehoek" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Dreieck" title="Dreieck – germană (Elveția)" lang="gsw" hreflang="gsw" data-title="Dreieck" data-language-autonym="Alemannisch" data-language-local-name="germană (Elveția)" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%B6%E1%88%B5%E1%89%B5_%E1%88%9B%E1%8A%A5%E1%8B%98%E1%8A%95" title="ሶስት ማእዘን – amharică" lang="am" hreflang="am" data-title="ሶስት ማእዘን" data-language-autonym="አማርኛ" data-language-local-name="amharică" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Trianglo" title="Trianglo – aragoneză" lang="an" hreflang="an" data-title="Trianglo" data-language-autonym="Aragonés" data-language-local-name="aragoneză" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ang mw-list-item"><a href="https://ang.wikipedia.org/wiki/%C3%9Er%C4%ABecge" title="Þrīecge – engleză veche" lang="ang" hreflang="ang" data-title="Þrīecge" data-language-autonym="Ænglisc" data-language-local-name="engleză veche" class="interlanguage-link-target"><span>Ænglisc</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AB%D9%84%D8%AB" title="مثلث – arabă" lang="ar" hreflang="ar" data-title="مثلث" data-language-autonym="العربية" data-language-local-name="arabă" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arc mw-list-item"><a href="https://arc.wikipedia.org/wiki/%DC%A1%DC%AC%DC%A0%DC%AC%DC%90" title="ܡܬܠܬܐ – aramaică" lang="arc" hreflang="arc" data-title="ܡܬܠܬܐ" data-language-autonym="ܐܪܡܝܐ" data-language-local-name="aramaică" class="interlanguage-link-target"><span>ܐܪܡܝܐ</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%85%D8%AA%D9%84%D8%AA" title="متلت – Moroccan Arabic" lang="ary" hreflang="ary" data-title="متلت" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%85%D8%AB%D9%84%D8%AB" title="مثلث – Egyptian Arabic" lang="arz" hreflang="arz" data-title="مثلث" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%A4%E0%A7%8D%E0%A7%B0%E0%A6%BF%E0%A6%AD%E0%A7%81%E0%A6%9C" title="ত্ৰিভুজ – asameză" lang="as" hreflang="as" data-title="ত্ৰিভুজ" data-language-autonym="অসমীয়া" data-language-local-name="asameză" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Tri%C3%A1ngulu" title="Triángulu – asturiană" lang="ast" hreflang="ast" data-title="Triángulu" data-language-autonym="Asturianu" data-language-local-name="asturiană" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ay mw-list-item"><a href="https://ay.wikipedia.org/wiki/Mujina" title="Mujina – aymara" lang="ay" hreflang="ay" data-title="Mujina" data-language-autonym="Aymar aru" data-language-local-name="aymara" class="interlanguage-link-target"><span>Aymar aru</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C3%9C%C3%A7bucaq" title="Üçbucaq – azeră" lang="az" hreflang="az" data-title="Üçbucaq" data-language-autonym="Azərbaycanca" data-language-local-name="azeră" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A7%D9%88%DA%86%E2%80%8C%D8%A8%D9%88%D8%AC%D8%A7%D9%82" title="اوچ‌بوجاق – South Azerbaijani" lang="azb" hreflang="azb" data-title="اوچ‌بوجاق" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D3%A8%D1%81%D0%BC%D3%A9%D0%B9%D3%A9%D1%88" title="Өсмөйөш – bașkiră" lang="ba" hreflang="ba" data-title="Өсмөйөш" data-language-autonym="Башҡортса" data-language-local-name="bașkiră" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Dreieck" title="Dreieck – Bavarian" lang="bar" hreflang="bar" data-title="Dreieck" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Tr%C4%97kompis" title="Trėkompis – Samogitian" lang="sgs" hreflang="sgs" data-title="Trėkompis" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Trianggulo" title="Trianggulo – Central Bikol" lang="bcl" hreflang="bcl" data-title="Trianggulo" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A2%D1%80%D0%BE%D1%85%D0%B2%D1%83%D0%B3%D0%BE%D0%BB%D1%8C%D0%BD%D1%96%D0%BA" title="Трохвугольнік – belarusă" lang="be" hreflang="be" data-title="Трохвугольнік" data-language-autonym="Беларуская" data-language-local-name="belarusă" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A2%D1%80%D1%8B%D0%BA%D1%83%D1%82%D0%BD%D1%96%D0%BA" title="Трыкутнік – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Трыкутнік" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D1%8A%D0%B3%D1%8A%D0%BB%D0%BD%D0%B8%D0%BA" title="Триъгълник – bulgară" lang="bg" hreflang="bg" data-title="Триъгълник" data-language-autonym="Български" data-language-local-name="bulgară" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%AD%E0%A5%81%E0%A4%9C" title="त्रिभुज – Bhojpuri" lang="bh" hreflang="bh" data-title="त्रिभुज" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A4%E0%A7%8D%E0%A6%B0%E0%A6%BF%E0%A6%AD%E0%A7%81%E0%A6%9C" title="ত্রিভুজ – bengaleză" lang="bn" hreflang="bn" data-title="ত্রিভুজ" data-language-autonym="বাংলা" data-language-local-name="bengaleză" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%A6%E0%BD%9F%E0%BD%B4%E0%BD%A2%E0%BC%8B%E0%BD%82%E0%BD%A6%E0%BD%B4%E0%BD%98%E0%BC%8B%E0%BD%91%E0%BD%96%E0%BD%96%E0%BE%B1%E0%BD%B2%E0%BC%8D" title="སཟུར་གསུམ་དབབྱི། – tibetană" lang="bo" hreflang="bo" data-title="སཟུར་གསུམ་དབབྱི།" data-language-autonym="བོད་ཡིག" data-language-local-name="tibetană" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Tric%27horn" title="Tric'horn – bretonă" lang="br" hreflang="br" data-title="Tric'horn" data-language-autonym="Brezhoneg" data-language-local-name="bretonă" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Trougao" title="Trougao – bosniacă" lang="bs" hreflang="bs" data-title="Trougao" data-language-autonym="Bosanski" data-language-local-name="bosniacă" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Triangle" title="Triangle – catalană" lang="ca" hreflang="ca" data-title="Triangle" data-language-autonym="Català" data-language-local-name="catalană" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/S%C4%83ng-g%C3%A1e%CC%A4k-h%C3%ACng" title="Săng-gáe̤k-hìng – Mindong" lang="cdo" hreflang="cdo" data-title="Săng-gáe̤k-hìng" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-chr mw-list-item"><a href="https://chr.wikipedia.org/wiki/%E1%8F%A6%E1%8E%A2_%E1%8F%A7%E1%8F%85%E1%8F%8F%E1%8F%AF_%E1%8E%A4%E1%8F%83%E1%8F%B4%E1%8E%A9" title="ᏦᎢ ᏧᏅᏏᏯ ᎤᏃᏴᎩ – cherokee" lang="chr" hreflang="chr" data-title="ᏦᎢ ᏧᏅᏏᏯ ᎤᏃᏴᎩ" data-language-autonym="ᏣᎳᎩ" data-language-local-name="cherokee" class="interlanguage-link-target"><span>ᏣᎳᎩ</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%B3%DB%8E%DA%AF%DB%86%D8%B4%DB%95" title="سێگۆشە – kurdă centrală" lang="ckb" hreflang="ckb" data-title="سێگۆشە" data-language-autonym="کوردی" data-language-local-name="kurdă centrală" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Triangulu" title="Triangulu – corsicană" lang="co" hreflang="co" data-title="Triangulu" data-language-autonym="Corsu" data-language-local-name="corsicană" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Troj%C3%BAheln%C3%ADk" title="Trojúhelník – cehă" lang="cs" hreflang="cs" data-title="Trojúhelník" data-language-autonym="Čeština" data-language-local-name="cehă" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-csb mw-list-item"><a href="https://csb.wikipedia.org/wiki/Trz%C3%ABn%C3%B3rt" title="Trzënórt – cașubiană" lang="csb" hreflang="csb" data-title="Trzënórt" data-language-autonym="Kaszëbsczi" data-language-local-name="cașubiană" class="interlanguage-link-target"><span>Kaszëbsczi</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%92%D0%B8%C3%A7%D0%BA%C4%95%D1%82%D0%B5%D1%81%D0%BB%C4%95%D1%85" title="Виçкĕтеслĕх – ciuvașă" lang="cv" hreflang="cv" data-title="Виçкĕтеслĕх" data-language-autonym="Чӑвашла" data-language-local-name="ciuvașă" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Triongl" title="Triongl – galeză" lang="cy" hreflang="cy" data-title="Triongl" data-language-autonym="Cymraeg" data-language-local-name="galeză" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Trekant" title="Trekant – daneză" lang="da" hreflang="da" data-title="Trekant" data-language-autonym="Dansk" data-language-local-name="daneză" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Dreieck" title="Dreieck – germană" lang="de" hreflang="de" data-title="Dreieck" data-language-autonym="Deutsch" data-language-local-name="germană" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Hir%C3%AAk%C4%B1nari" title="Hirêkınari – Zazaki" lang="diq" hreflang="diq" data-title="Hirêkınari" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-dsb mw-list-item"><a href="https://dsb.wikipedia.org/wiki/T%C5%9Biro%C5%BEk" title="Tśirožk – sorabă de jos" lang="dsb" hreflang="dsb" data-title="Tśirožk" data-language-autonym="Dolnoserbski" data-language-local-name="sorabă de jos" class="interlanguage-link-target"><span>Dolnoserbski</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A4%CF%81%CE%AF%CE%B3%CF%89%CE%BD%CE%BF" title="Τρίγωνο – greacă" lang="el" hreflang="el" data-title="Τρίγωνο" data-language-autonym="Ελληνικά" data-language-local-name="greacă" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Triangle" title="Triangle – engleză" lang="en" hreflang="en" data-title="Triangle" data-language-autonym="English" data-language-local-name="engleză" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Triangulo" title="Triangulo – esperanto" lang="eo" hreflang="eo" data-title="Triangulo" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Tri%C3%A1ngulo" title="Triángulo – spaniolă" lang="es" hreflang="es" data-title="Triángulo" data-language-autonym="Español" data-language-local-name="spaniolă" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kolmnurk" title="Kolmnurk – estonă" lang="et" hreflang="et" data-title="Kolmnurk" data-language-autonym="Eesti" data-language-local-name="estonă" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Triangelu" title="Triangelu – bască" lang="eu" hreflang="eu" data-title="Triangelu" data-language-autonym="Euskara" data-language-local-name="bască" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%AB%D9%84%D8%AB" title="مثلث – persană" lang="fa" hreflang="fa" data-title="مثلث" data-language-autonym="فارسی" data-language-local-name="persană" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kolmio" title="Kolmio – finlandeză" lang="fi" hreflang="fi" data-title="Kolmio" data-language-autonym="Suomi" data-language-local-name="finlandeză" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Kolmnukk" title="Kolmnukk – Võro" lang="vro" hreflang="vro" data-title="Kolmnukk" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Tututolu" title="Tututolu – fijiană" lang="fj" hreflang="fj" data-title="Tututolu" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fijiană" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Tr%C3%ADkantur" title="Tríkantur – feroeză" lang="fo" hreflang="fo" data-title="Tríkantur" data-language-autonym="Føroyskt" data-language-local-name="feroeză" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Triangle" title="Triangle – franceză" lang="fr" hreflang="fr" data-title="Triangle" data-language-autonym="Français" data-language-local-name="franceză" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Triihuk" title="Triihuk – frizonă nordică" lang="frr" hreflang="frr" data-title="Triihuk" data-language-autonym="Nordfriisk" data-language-local-name="frizonă nordică" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Triant%C3%A1n_(c%C3%A9imseata)" title="Triantán (céimseata) – irlandeză" lang="ga" hreflang="ga" data-title="Triantán (céimseata)" data-language-autonym="Gaeilge" data-language-local-name="irlandeză" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E4%B8%89%E8%A7%92%E5%BD%A2" title="三角形 – chineză gan" lang="gan" hreflang="gan" data-title="三角形" data-language-autonym="贛語" data-language-local-name="chineză gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Triyang" title="Triyang – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Triyang" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Tri%C3%A1ngulo" title="Triángulo – galiciană" lang="gl" hreflang="gl" data-title="Triángulo" data-language-autonym="Galego" data-language-local-name="galiciană" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%A4%E0%AB%8D%E0%AA%B0%E0%AA%BF%E0%AA%95%E0%AB%8B%E0%AA%A3" title="ત્રિકોણ – gujarati" lang="gu" hreflang="gu" data-title="ત્રિકોણ" data-language-autonym="ગુજરાતી" data-language-local-name="gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-guc mw-list-item"><a href="https://guc.wikipedia.org/wiki/Ap%C3%BCn%C3%BCinsheke%27einr%C3%BC" title="Apünüinsheke'einrü – Wayuu" lang="guc" hreflang="guc" data-title="Apünüinsheke'einrü" data-language-autonym="Wayuunaiki" data-language-local-name="Wayuu" class="interlanguage-link-target"><span>Wayuunaiki</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Troorane" title="Troorane – manx" lang="gv" hreflang="gv" data-title="Troorane" data-language-autonym="Gaelg" data-language-local-name="manx" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/S%C3%A2m-kok-h%C3%ACn" title="Sâm-kok-hìn – chineză hakka" lang="hak" hreflang="hak" data-title="Sâm-kok-hìn" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="chineză hakka" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A9%D7%95%D7%9C%D7%A9" title="משולש – ebraică" lang="he" hreflang="he" data-title="משולש" data-language-autonym="עברית" data-language-local-name="ebraică" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%AD%E0%A5%81%E0%A4%9C" title="त्रिभुज – hindi" lang="hi" hreflang="hi" data-title="त्रिभुज" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Trokut" title="Trokut – croată" lang="hr" hreflang="hr" data-title="Trokut" data-language-autonym="Hrvatski" data-language-local-name="croată" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hsb mw-list-item"><a href="https://hsb.wikipedia.org/wiki/T%C5%99ir%C3%B3%C5%BEk" title="Třiróžk – sorabă de sus" lang="hsb" hreflang="hsb" data-title="Třiróžk" data-language-autonym="Hornjoserbsce" data-language-local-name="sorabă de sus" class="interlanguage-link-target"><span>Hornjoserbsce</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Triyang" title="Triyang – haitiană" lang="ht" hreflang="ht" data-title="Triyang" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitiană" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/H%C3%A1romsz%C3%B6g" title="Háromszög – maghiară" lang="hu" hreflang="hu" data-title="Háromszög" data-language-autonym="Magyar" data-language-local-name="maghiară" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B5%D5%BC%D5%A1%D5%B6%D5%AF%D5%B5%D5%B8%D6%82%D5%B6" title="Եռանկյուն – armeană" lang="hy" hreflang="hy" data-title="Եռանկյուն" data-language-autonym="Հայերեն" data-language-local-name="armeană" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Triangulo" title="Triangulo – interlingua" lang="ia" hreflang="ia" data-title="Triangulo" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Segitiga" title="Segitiga – indoneziană" lang="id" hreflang="id" data-title="Segitiga" data-language-autonym="Bahasa Indonesia" data-language-local-name="indoneziană" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Triangulo" title="Triangulo – ido" lang="io" hreflang="io" data-title="Triangulo" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/%C3%9Er%C3%ADhyrningur" title="Þríhyrningur – islandeză" lang="is" hreflang="is" data-title="Þríhyrningur" data-language-autonym="Íslenska" data-language-local-name="islandeză" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Triangolo" title="Triangolo – italiană" lang="it" hreflang="it" data-title="Triangolo" data-language-autonym="Italiano" data-language-local-name="italiană" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%B8%89%E8%A7%92%E5%BD%A2" title="三角形 – japoneză" lang="ja" hreflang="ja" data-title="三角形" data-language-autonym="日本語" data-language-local-name="japoneză" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Chrayanggl" title="Chrayanggl – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Chrayanggl" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Pasagi_telu" title="Pasagi telu – javaneză" lang="jv" hreflang="jv" data-title="Pasagi telu" data-language-autonym="Jawa" data-language-local-name="javaneză" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka badge-Q17437796 badge-featuredarticle mw-list-item" title="articol de calitate"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%90%E1%83%9B%E1%83%99%E1%83%A3%E1%83%97%E1%83%AE%E1%83%94%E1%83%93%E1%83%98" title="სამკუთხედი – georgiană" lang="ka" hreflang="ka" data-title="სამკუთხედი" data-language-autonym="ქართული" data-language-local-name="georgiană" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/%C3%9Ashm%C3%BAyeshlik" title="Úshmúyeshlik – karakalpak" lang="kaa" hreflang="kaa" data-title="Úshmúyeshlik" data-language-autonym="Qaraqalpaqsha" data-language-local-name="karakalpak" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-kbd mw-list-item"><a href="https://kbd.wikipedia.org/wiki/%D0%A9%D0%B8%D0%BC%D1%8D" title="Щимэ – kabardian" lang="kbd" hreflang="kbd" data-title="Щимэ" data-language-autonym="Адыгэбзэ" data-language-local-name="kabardian" class="interlanguage-link-target"><span>Адыгэбзэ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D2%AE%D1%88%D0%B1%D2%B1%D1%80%D1%8B%D1%88" title="Үшбұрыш – kazahă" lang="kk" hreflang="kk" data-title="Үшбұрыш" data-language-autonym="Қазақша" data-language-local-name="kazahă" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km badge-Q17437796 badge-featuredarticle mw-list-item" title="articol de calitate"><a href="https://km.wikipedia.org/wiki/%E1%9E%8F%E1%9F%92%E1%9E%9A%E1%9E%B8%E1%9E%80%E1%9F%84%E1%9E%8E" title="ត្រីកោណ – khmeră" lang="km" hreflang="km" data-title="ត្រីកោណ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="khmeră" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%A4%E0%B3%8D%E0%B2%B0%E0%B2%BF%E0%B2%95%E0%B3%8B%E0%B2%A8" title="ತ್ರಿಕೋನ – kannada" lang="kn" hreflang="kn" data-title="ತ್ರಿಕೋನ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%82%BC%EA%B0%81%ED%98%95" title="삼각형 – coreeană" lang="ko" hreflang="ko" data-title="삼각형" data-language-autonym="한국어" data-language-local-name="coreeană" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/S%C3%AAgo%C5%9Fe" title="Sêgoşe – kurdă" lang="ku" hreflang="ku" data-title="Sêgoşe" data-language-autonym="Kurdî" data-language-local-name="kurdă" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Trihorn" title="Trihorn – cornică" lang="kw" hreflang="kw" data-title="Trihorn" data-language-autonym="Kernowek" data-language-local-name="cornică" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D2%AE%D1%87_%D0%B1%D1%83%D1%80%D1%87%D1%82%D1%83%D0%BA" title="Үч бурчтук – kârgâză" lang="ky" hreflang="ky" data-title="Үч бурчтук" data-language-autonym="Кыргызча" data-language-local-name="kârgâză" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Triangulum" title="Triangulum – latină" lang="la" hreflang="la" data-title="Triangulum" data-language-autonym="Latina" data-language-local-name="latină" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Triangulo" title="Triangulo – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Triangulo" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Driehook" title="Driehook – limburgheză" lang="li" hreflang="li" data-title="Driehook" data-language-autonym="Limburgs" data-language-local-name="limburgheză" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Triangolo" title="Triangolo – liguriană" lang="lij" hreflang="lij" data-title="Triangolo" data-language-autonym="Ligure" data-language-local-name="liguriană" class="interlanguage-link-target"><span>Ligure</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Tri%C3%A0ngol" title="Triàngol – Lombard" lang="lmo" hreflang="lmo" data-title="Triàngol" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-ln mw-list-item"><a href="https://ln.wikipedia.org/wiki/Mpanzi-mis%C3%A1to" title="Mpanzi-misáto – lingala" lang="ln" hreflang="ln" data-title="Mpanzi-misáto" data-language-autonym="Lingála" data-language-local-name="lingala" class="interlanguage-link-target"><span>Lingála</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%AE%E0%BA%B9%E0%BA%9A%E0%BA%AA%E0%BA%B2%E0%BA%A1%E0%BB%81%E0%BA%88" title="ຮູບສາມແຈ – laoțiană" lang="lo" hreflang="lo" data-title="ຮູບສາມແຈ" data-language-autonym="ລາວ" data-language-local-name="laoțiană" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Trikampis" title="Trikampis – lituaniană" lang="lt" hreflang="lt" data-title="Trikampis" data-language-autonym="Lietuvių" data-language-local-name="lituaniană" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Trijst%C5%ABris" title="Trijstūris – letonă" lang="lv" hreflang="lv" data-title="Trijstūris" data-language-autonym="Latviešu" data-language-local-name="letonă" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Telolafy" title="Telolafy – malgașă" lang="mg" hreflang="mg" data-title="Telolafy" data-language-autonym="Malagasy" data-language-local-name="malgașă" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%9A%D1%83%D0%BC%D0%BB%D1%83%D0%BA" title="Кумлук – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Кумлук" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Sagitigo" title="Sagitigo – minangkabau" lang="min" hreflang="min" data-title="Sagitigo" data-language-autonym="Minangkabau" data-language-local-name="minangkabau" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B0%D0%B3%D0%BE%D0%BB%D0%BD%D0%B8%D0%BA" title="Триаголник – macedoneană" lang="mk" hreflang="mk" data-title="Триаголник" data-language-autonym="Македонски" data-language-local-name="macedoneană" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%A4%E0%B5%8D%E0%B4%B0%E0%B4%BF%E0%B4%95%E0%B5%8B%E0%B4%A3%E0%B4%82" title="ത്രികോണം – malayalam" lang="ml" hreflang="ml" data-title="ത്രികോണം" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn badge-Q17437796 badge-featuredarticle mw-list-item" title="articol de calitate"><a href="https://mn.wikipedia.org/wiki/%D0%93%D1%83%D1%80%D0%B2%D0%B0%D0%BB%D0%B6%D0%B8%D0%BD" title="Гурвалжин – mongolă" lang="mn" hreflang="mn" data-title="Гурвалжин" data-language-autonym="Монгол" data-language-local-name="mongolă" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A5%8B%E0%A4%A3" title="त्रिकोण – marathi" lang="mr" hreflang="mr" data-title="त्रिकोण" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Segi_tiga" title="Segi tiga – malaeză" lang="ms" hreflang="ms" data-title="Segi tiga" data-language-autonym="Bahasa Melayu" data-language-local-name="malaeză" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Trijangolu" title="Trijangolu – malteză" lang="mt" hreflang="mt" data-title="Trijangolu" data-language-autonym="Malti" data-language-local-name="malteză" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%90%E1%80%BC%E1%80%AD%E1%80%82%E1%80%B6" title="တြိဂံ – birmană" lang="my" hreflang="my" data-title="တြိဂံ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmană" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%AD%E0%A5%81%E0%A4%9C" title="त्रिभुज – nepaleză" lang="ne" hreflang="ne" data-title="त्रिभुज" data-language-autonym="नेपाली" data-language-local-name="nepaleză" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%B8%E0%A5%8D%E0%A4%B5%E0%A4%95%E0%A5%81%E0%A4%82" title="स्वकुं – newari" lang="new" hreflang="new" data-title="स्वकुं" data-language-autonym="नेपाल भाषा" data-language-local-name="newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Driehoek_(meetkunde)" title="Driehoek (meetkunde) – neerlandeză" lang="nl" hreflang="nl" data-title="Driehoek (meetkunde)" data-language-autonym="Nederlands" data-language-local-name="neerlandeză" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Trekant" title="Trekant – norvegiană nynorsk" lang="nn" hreflang="nn" data-title="Trekant" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegiană nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Trekant" title="Trekant – norvegiană bokmål" lang="nb" hreflang="nb" data-title="Trekant" data-language-autonym="Norsk bokmål" data-language-local-name="norvegiană bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nrm mw-list-item"><a href="https://nrm.wikipedia.org/wiki/Trian" title="Trian – Norman" lang="nrf" hreflang="nrf" data-title="Trian" data-language-autonym="Nouormand" data-language-local-name="Norman" class="interlanguage-link-target"><span>Nouormand</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Triangle" title="Triangle – occitană" lang="oc" hreflang="oc" data-title="Triangle" data-language-autonym="Occitan" data-language-local-name="occitană" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%A4%E0%AD%8D%E0%AC%B0%E0%AC%BF%E0%AC%AD%E0%AD%81%E0%AC%9C" title="ତ୍ରିଭୁଜ – odia" lang="or" hreflang="or" data-title="ତ୍ରିଭୁଜ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="odia" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%A4%E0%A8%BF%E0%A8%95%E0%A9%8B%E0%A8%A8" title="ਤਿਕੋਨ – punjabi" lang="pa" hreflang="pa" data-title="ਤਿਕੋਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pfl mw-list-item"><a href="https://pfl.wikipedia.org/wiki/Dreieck" title="Dreieck – Palatine German" lang="pfl" hreflang="pfl" data-title="Dreieck" data-language-autonym="Pälzisch" data-language-local-name="Palatine German" class="interlanguage-link-target"><span>Pälzisch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Tr%C3%B3jk%C4%85t" title="Trójkąt – poloneză" lang="pl" hreflang="pl" data-title="Trójkąt" data-language-autonym="Polski" data-language-local-name="poloneză" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%AA%DA%A9%D9%88%D9%86" title="تکون – Western Punjabi" lang="pnb" hreflang="pnb" data-title="تکون" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%AF%D8%B1%DB%90%DA%85%D9%86%DA%89%DB%8C" title="درېڅنډی – paștună" lang="ps" hreflang="ps" data-title="درېڅنډی" data-language-autonym="پښتو" data-language-local-name="paștună" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Tri%C3%A2ngulo" title="Triângulo – portugheză" lang="pt" hreflang="pt" data-title="Triângulo" data-language-autonym="Português" data-language-local-name="portugheză" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Kimsak%27uchu" title="Kimsak'uchu – quechua" lang="qu" hreflang="qu" data-title="Kimsak'uchu" data-language-autonym="Runa Simi" data-language-local-name="quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D1%80%D0%B5%D1%83%D0%B3%D0%BE%D0%BB%D1%8C%D0%BD%D0%B8%D0%BA" title="Треугольник – rusă" lang="ru" hreflang="ru" data-title="Треугольник" data-language-autonym="Русский" data-language-local-name="rusă" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D1%83%D0%B3%D0%BE%D0%BB%D0%BD%D0%B8%D0%BA" title="Триуголник – Rusyn" lang="rue" hreflang="rue" data-title="Триуголник" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Tri%C3%A0nculu" title="Triànculu – siciliană" lang="scn" hreflang="scn" data-title="Triànculu" data-language-autonym="Sicilianu" data-language-local-name="siciliană" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Triangle" title="Triangle – scots" lang="sco" hreflang="sco" data-title="Triangle" data-language-autonym="Scots" data-language-local-name="scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D9%BD%DA%AA%D9%86%DA%8A%D9%88" title="ٽڪنڊو – sindhi" lang="sd" hreflang="sd" data-title="ٽڪنڊو" data-language-autonym="سنڌي" data-language-local-name="sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-se mw-list-item"><a href="https://se.wikipedia.org/wiki/Golmma%C4%8Diegat" title="Golmmačiegat – sami de nord" lang="se" hreflang="se" data-title="Golmmačiegat" data-language-autonym="Davvisámegiella" data-language-local-name="sami de nord" class="interlanguage-link-target"><span>Davvisámegiella</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Trokut" title="Trokut – sârbo-croată" lang="sh" hreflang="sh" data-title="Trokut" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="sârbo-croată" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%AD%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%92%E0%B6%9A%E0%B7%9D%E0%B6%AB" title="ත්‍රිකෝණ – singhaleză" lang="si" hreflang="si" data-title="ත්‍රිකෝණ" data-language-autonym="සිංහල" data-language-local-name="singhaleză" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Triangle" title="Triangle – Simple English" lang="en-simple" hreflang="en-simple" data-title="Triangle" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Trojuholn%C3%ADk" title="Trojuholník – slovacă" lang="sk" hreflang="sk" data-title="Trojuholník" data-language-autonym="Slovenčina" data-language-local-name="slovacă" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Trikotnik" title="Trikotnik – slovenă" lang="sl" hreflang="sl" data-title="Trikotnik" data-language-autonym="Slovenščina" data-language-local-name="slovenă" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-smn mw-list-item"><a href="https://smn.wikipedia.org/wiki/Kulm%C3%A2h%C3%A2%C5%A1" title="Kulmâhâš – sami inari" lang="smn" hreflang="smn" data-title="Kulmâhâš" data-language-autonym="Anarâškielâ" data-language-local-name="sami inari" class="interlanguage-link-target"><span>Anarâškielâ</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Gonyonhatu" title="Gonyonhatu – shona" lang="sn" hreflang="sn" data-title="Gonyonhatu" data-language-autonym="ChiShona" data-language-local-name="shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Saddexagal" title="Saddexagal – somaleză" lang="so" hreflang="so" data-title="Saddexagal" data-language-autonym="Soomaaliga" data-language-local-name="somaleză" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Trek%C3%ABnd%C3%ABshi" title="Trekëndëshi – albaneză" lang="sq" hreflang="sq" data-title="Trekëndëshi" data-language-autonym="Shqip" data-language-local-name="albaneză" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A2%D1%80%D0%BE%D1%83%D0%B3%D0%B0%D0%BE" title="Троугао – sârbă" lang="sr" hreflang="sr" data-title="Троугао" data-language-autonym="Српски / srpski" data-language-local-name="sârbă" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Juru_tilu" title="Juru tilu – sundaneză" lang="su" hreflang="su" data-title="Juru tilu" data-language-autonym="Sunda" data-language-local-name="sundaneză" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Triangel" title="Triangel – suedeză" lang="sv" hreflang="sv" data-title="Triangel" data-language-autonym="Svenska" data-language-local-name="suedeză" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Pembetatu" title="Pembetatu – swahili" lang="sw" hreflang="sw" data-title="Pembetatu" data-language-autonym="Kiswahili" data-language-local-name="swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Trziek" title="Trziek – Silesian" lang="szl" hreflang="szl" data-title="Trziek" data-language-autonym="Ślůnski" data-language-local-name="Silesian" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AF%81%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AF%8B%E0%AE%A3%E0%AE%AE%E0%AF%8D" title="முக்கோணம் – tamilă" lang="ta" hreflang="ta" data-title="முக்கோணம்" data-language-autonym="தமிழ்" data-language-local-name="tamilă" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%A4%E0%B1%8D%E0%B0%B0%E0%B0%BF%E0%B0%AD%E0%B1%81%E0%B0%9C%E0%B0%82" title="త్రిభుజం – telugu" lang="te" hreflang="te" data-title="త్రిభుజం" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%A1%D0%B5%D0%BA%D1%83%D0%BD%D2%B7%D0%B0" title="Секунҷа – tadjică" lang="tg" hreflang="tg" data-title="Секунҷа" data-language-autonym="Тоҷикӣ" data-language-local-name="tadjică" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A3%E0%B8%B9%E0%B8%9B%E0%B8%AA%E0%B8%B2%E0%B8%A1%E0%B9%80%E0%B8%AB%E0%B8%A5%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%A1" title="รูปสามเหลี่ยม – thailandeză" lang="th" hreflang="th" data-title="รูปสามเหลี่ยม" data-language-autonym="ไทย" data-language-local-name="thailandeză" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Tatsulok" title="Tatsulok – tagalog" lang="tl" hreflang="tl" data-title="Tatsulok" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%9C%C3%A7gen" title="Üçgen – turcă" lang="tr" hreflang="tr" data-title="Üçgen" data-language-autonym="Türkçe" data-language-local-name="turcă" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D3%A8%D1%87%D0%BF%D0%BE%D1%87%D0%BC%D0%B0%D0%BA" title="Өчпочмак – tătară" lang="tt" hreflang="tt" data-title="Өчпочмак" data-language-autonym="Татарча / tatarça" data-language-local-name="tătară" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%BA%D1%83%D1%82%D0%BD%D0%B8%D0%BA" title="Трикутник – ucraineană" lang="uk" hreflang="uk" data-title="Трикутник" data-language-autonym="Українська" data-language-local-name="ucraineană" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D8%AB%D9%84%D8%AB" title="مثلث – urdu" lang="ur" hreflang="ur" data-title="مثلث" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Uchburchak" title="Uchburchak – uzbecă" lang="uz" hreflang="uz" data-title="Uchburchak" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbecă" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Triango%C5%82o" title="Triangoło – venetă" lang="vec" hreflang="vec" data-title="Triangoło" data-language-autonym="Vèneto" data-language-local-name="venetă" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Tam_gi%C3%A1c" title="Tam giác – vietnameză" lang="vi" hreflang="vi" data-title="Tam giác" data-language-autonym="Tiếng Việt" data-language-local-name="vietnameză" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Drieoek" title="Drieoek – West Flemish" lang="vls" hreflang="vls" data-title="Drieoek" data-language-autonym="West-Vlams" data-language-local-name="West Flemish" class="interlanguage-link-target"><span>West-Vlams</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Trayanggulo" title="Trayanggulo – waray" lang="war" hreflang="war" data-title="Trayanggulo" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E4%B8%89%E8%A7%92%E5%BD%A2" title="三角形 – chineză wu" lang="wuu" hreflang="wuu" data-title="三角形" data-language-autonym="吴语" data-language-local-name="chineză wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%93%D7%A8%D7%99%D7%99%D7%A2%D7%A7" title="דרייעק – idiș" lang="yi" hreflang="yi" data-title="דרייעק" data-language-autonym="ייִדיש" data-language-local-name="idiș" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/An%C3%ADgunm%E1%BA%B9%CC%81ta" title="Anígunmẹ́ta – yoruba" lang="yo" hreflang="yo" data-title="Anígunmẹ́ta" data-language-autonym="Yorùbá" data-language-local-name="yoruba" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zgh mw-list-item"><a href="https://zgh.wikipedia.org/wiki/%E2%B4%B0%E2%B5%8E%E2%B4%BD%E2%B5%95%E2%B4%B0%E2%B4%B9" title="ⴰⵎⴽⵕⴰⴹ – tamazight standard marocană" lang="zgh" hreflang="zgh" data-title="ⴰⵎⴽⵕⴰⴹ" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="tamazight standard marocană" class="interlanguage-link-target"><span>ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%B8%89%E8%A7%92%E5%BD%A2" title="三角形 – chineză" lang="zh" hreflang="zh" data-title="三角形" data-language-autonym="中文" data-language-local-name="chineză" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E4%B8%89%E8%A7%92%E5%BD%A2" title="三角形 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="三角形" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Sa%E2%81%BF-kak-h%C3%AAng" title="Saⁿ-kak-hêng – chineză min nan" lang="nan" hreflang="nan" data-title="Saⁿ-kak-hêng" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="chineză min nan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%B8%89%E8%A7%92%E5%BD%A2" title="三角形 – cantoneză" lang="yue" hreflang="yue" data-title="三角形" data-language-autonym="粵語" data-language-local-name="cantoneză" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q19821#sitelinks-wikipedia" title="Modifică legăturile interlinguale" 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.mw-parser-output .ambox-speedy,html.skin-theme-clientpref-os .mw-parser-output .ambox-delete{border-left:10px solid #070101!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-content{border-left:10px solid #261500!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-style{border-left:10px solid #544004!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-move{border-left:10px solid #1e0a28!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-protection{border-left:10px solid #bba!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-notice,html.skin-theme-clientpref-os .mw-parser-output .ambox-delete,html.skin-theme-clientpref-os .mw-parser-output .ambox-content,html.skin-theme-clientpref-os .mw-parser-output .ambox-style,html.skin-theme-clientpref-os .mw-parser-output .ambox-move,html.skin-theme-clientpref-os .mw-parser-output .ambox-protection{background-color:#202122!important}}</style><table class="metadata plainlinks ambox ambox ambox-style ambox-style" style=""> <tbody><tr><td class="mbox-image"><div style="width: 52px;"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Text_document_with_red_question_mark.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/50px-Text_document_with_red_question_mark.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/75px-Text_document_with_red_question_mark.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/100px-Text_document_with_red_question_mark.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span></div></td><td class="mbox-text" style=""><span class="mbox-text-span">Deși acest articol conține o listă de referințe bibliografice, <a href="/wiki/Wikipedia:Verificabilitate" title="Wikipedia:Verificabilitate">sursele</a> sale rămân neclare deoarece îi lipsesc <a href="/wiki/Wikipedia:Citarea_surselor#.E2.80.9ENote.E2.80.9D" title="Wikipedia:Citarea surselor">notele de subsol</a>.<br /> Puteți ajuta introducând <a href="/wiki/Ajutor:Note" title="Ajutor:Note">citări mai precise</a> ale surselor.<span class="hide-when-compact"> </span><span class="hide-when-compact"> </span></span></td></tr></tbody></table> <table class="infobox" cellspacing="5" style="width: 22em; text-align: left; font-size: 88%; line-height: 1.5em;"> <tbody><tr><td colspan="2" class="" style="text-align:center; font-size: 125%; font-weight: bold; background:#e7dcc3;">Triunghi</td></tr><tr><td colspan="2" class="" style="text-align:center;"> <span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/Fi%C8%99ier:Triangle_illustration.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Triangle_illustration.svg/220px-Triangle_illustration.svg.png" decoding="async" width="220" height="248" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Triangle_illustration.svg/330px-Triangle_illustration.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/45/Triangle_illustration.svg/440px-Triangle_illustration.svg.png 2x" data-file-width="512" data-file-height="576" /></a></span> <br /> <span style="">Imagine</span></td></tr><tr><th style=""><a href="/wiki/Latur%C4%83_(geometrie)" title="Latură (geometrie)">Laturi</a> și <a href="/wiki/V%C3%A2rf_(geometrie)" title="Vârf (geometrie)">vârfuri</a></th><td class="" style="">3</td></tr><tr><th style=""><a href="/wiki/Simbol_Schl%C3%A4fli" title="Simbol Schläfli">Simbol Schläfli</a></th><td class="" style="">{3} (pt. <a href="/wiki/Triunghi_echilateral" title="Triunghi echilateral">echilateral</a>)</td></tr><tr><th style=""><a href="/wiki/Diagram%C4%83_Coxeter%E2%80%93Dynkin" title="Diagramă Coxeter–Dynkin">Diagramă Coxeter</a></th><td class="" style=""><span style="display:inline-block;"><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png" decoding="async" width="9" height="23" class="mw-file-element" data-file-width="9" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png" decoding="async" width="6" height="23" class="mw-file-element" data-file-width="6" data-file-height="23" /></span></span><span class="mw-default-size" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png" decoding="async" width="5" height="23" class="mw-file-element" data-file-width="5" data-file-height="23" /></span></span></span></td></tr><tr><th style=""><a href="/wiki/Grup_de_simetrie" title="Grup de simetrie">Grup de simetrie</a></th><td class="" style=""><a href="/w/index.php?title=Dihedral_group&action=edit&redlink=1" class="new" title="Dihedral group — pagină inexistentă">Dih<sub>3</sub></a> [3], 2*3</td></tr><tr><th style=""><a href="/wiki/Arie" title="Arie">Arie</a></th><td class="" style="">diverse metode</td></tr><tr><th style=""><a href="/wiki/Unghi_interior" title="Unghi interior">Unghi interior</a> (grade)</th><td class="" style="">60° (pt. echilateral)</td></tr><tr><th style="">Proprietăți</th><td class="" style=""><a href="/wiki/Convexitate" title="Convexitate">convex</a></td></tr> </tbody></table> <div role="note" class="dezambiguizare">Pentru alte sensuri, vedeți <a href="/wiki/Triunghi_(dezambiguizare)" class="mw-disambig" title="Triunghi (dezambiguizare)">Triunghi (dezambiguizare)</a>.</div> <p><b>Triunghiul</b> este <a href="/wiki/Figur%C4%83_geometric%C4%83" class="mw-redirect" title="Figură geometrică">figura geometrică</a> dată de <a href="/wiki/Reuniune_(matematic%C4%83)" title="Reuniune (matematică)">reuniunea</a> <a href="/wiki/Segment_(geometrie)" title="Segment (geometrie)">segmentelor</a> închise determinate de trei <a href="/wiki/Punct_(geometrie)" title="Punct (geometrie)">puncte</a> distincte <a href="/wiki/Coliniaritate" title="Coliniaritate">necoliniare</a>. Este una dintre <a href="/wiki/Form%C4%83" title="Formă">formele</a> <a href="/wiki/Poligon" title="Poligon">poligonale</a> fundamentale ale <a href="/wiki/Geometrie" title="Geometrie">geometriei</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definiții"><span id="Defini.C8.9Bii"></span>Definiții</h2></div> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [AB]\cup [BC]\cup [CA]=\triangle [ABC]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>A</mi> <mi>B</mi> <mo stretchy="false">]</mo> <mo>∪</mo> <mo stretchy="false">[</mo> <mi>B</mi> <mi>C</mi> <mo stretchy="false">]</mo> <mo>∪</mo> <mo stretchy="false">[</mo> <mi>C</mi> <mi>A</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mi mathvariant="normal">△</mi> <mo stretchy="false">[</mo> <mi>A</mi> <mi>B</mi> <mi>C</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [AB]\cup [BC]\cup [CA]=\triangle [ABC]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8b4fc29b17a8101104eb534922becd82eb4e876" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:31.325ex; height:2.843ex;" alt="{\displaystyle [AB]\cup [BC]\cup [CA]=\triangle [ABC]}"></span> </p> <ul><li>punctele <i>A, B, C</i> se numesc vârfurile triunghiului.</li> <li><i>[AB], [BC], [AC]</i> se numesc laturile triunghiului.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \angle BAC,\angle ABC,\angle ACB}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∠</mi> <mi>B</mi> <mi>A</mi> <mi>C</mi> <mo>,</mo> <mi mathvariant="normal">∠</mi> <mi>A</mi> <mi>B</mi> <mi>C</mi> <mo>,</mo> <mi mathvariant="normal">∠</mi> <mi>A</mi> <mi>C</mi> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \angle BAC,\angle ABC,\angle ACB}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4e11c10266bb58c2c17d5959e7eb4ff8a3d520c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:22.922ex; height:2.509ex;" alt="{\displaystyle \angle BAC,\angle ABC,\angle ACB}"></span> se numesc unghiurile (interne) triunghiului.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Clasificare">Clasificare</h2></div> <p>Clasificarea triunghiurilor se face: </p> <ul><li>în funcție de lungimile laturilor</li> <li>după felul unghiurilor</li></ul> <div class="mw-heading mw-heading3"><h3 id="În_funcție_de_lungimile_laturilor"><span id=".C3.8En_func.C8.9Bie_de_lungimile_laturilor"></span>În funcție de lungimile laturilor</h3></div> <p>Un triunghi cu toate laturile congruente se numește <i><a href="/wiki/Triunghi_echilateral" title="Triunghi echilateral">triunghi echilateral</a></i>. Un triunghi cu două laturi congruente se numește <i><a href="/wiki/Triunghi_isoscel" title="Triunghi isoscel">triunghi isoscel</a></i>. Un triunghi care are laturile de lungimi diferite se numește <i>triunghi scalen</i> (sau <i>oarecare</i>). </p> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Triangle.Equilateral.svg" class="mw-file-description" title="Triunghi echilateral"><img alt="Triunghi echilateral" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Triangle.Equilateral.svg/120px-Triangle.Equilateral.svg.png" decoding="async" width="120" height="97" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Triangle.Equilateral.svg/180px-Triangle.Equilateral.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Triangle.Equilateral.svg/240px-Triangle.Equilateral.svg.png 2x" data-file-width="512" data-file-height="415" /></a></span></div> <div class="gallerytext">Triunghi echilateral</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Triangle.Isosceles.svg" class="mw-file-description" title="Triunghi isoscel"><img alt="Triunghi isoscel" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Triangle.Isosceles.svg/78px-Triangle.Isosceles.svg.png" decoding="async" width="78" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Triangle.Isosceles.svg/117px-Triangle.Isosceles.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/14/Triangle.Isosceles.svg/156px-Triangle.Isosceles.svg.png 2x" data-file-width="74" data-file-height="114" /></a></span></div> <div class="gallerytext">Triunghi isoscel</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Triangle.Scalene.svg" class="mw-file-description" title="Triunghi scalen"><img alt="Triunghi scalen" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Triangle.Scalene.svg/120px-Triangle.Scalene.svg.png" decoding="async" width="120" height="54" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Triangle.Scalene.svg/180px-Triangle.Scalene.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/93/Triangle.Scalene.svg/240px-Triangle.Scalene.svg.png 2x" data-file-width="245" data-file-height="110" /></a></span></div> <div class="gallerytext">Triunghi scalen</div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="După_felul_unghiurilor"><span id="Dup.C4.83_felul_unghiurilor"></span>După felul unghiurilor</h3></div> <p>Triunghiul cu toate unghiurile ascuțite este numit <i>triunghi ascuțitunghic</i>. Dacă unul dintre unghiuri este drept, triunghiul este denumit <i><a href="/wiki/Triunghi_dreptunghic" title="Triunghi dreptunghic">dreptunghic</a></i>. Triunghiul cu un unghi mai mare de 90<sup>0</sup> se numește <i>triunghi obtuzunghic</i>. </p> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Triangle.Right.svg" class="mw-file-description" title="Triunghi dreptunghic."><img alt="Triunghi dreptunghic." src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Triangle.Right.svg/120px-Triangle.Right.svg.png" decoding="async" width="120" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Triangle.Right.svg/180px-Triangle.Right.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/Triangle.Right.svg/240px-Triangle.Right.svg.png 2x" data-file-width="150" data-file-height="113" /></a></span></div> <div class="gallerytext">Triunghi dreptunghic.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Triangle.Obtuse.svg" class="mw-file-description" title="Triunghi obtuzunghic."><img alt="Triunghi obtuzunghic." src="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Triangle.Obtuse.svg/120px-Triangle.Obtuse.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Triangle.Obtuse.svg/180px-Triangle.Obtuse.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/05/Triangle.Obtuse.svg/240px-Triangle.Obtuse.svg.png 2x" data-file-width="113" data-file-height="113" /></a></span></div> <div class="gallerytext">Triunghi obtuzunghic.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Triangle.Acute.svg" class="mw-file-description" title="Triunghi ascuțitunghic."><img alt="Triunghi ascuțitunghic." src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Triangle.Acute.svg/120px-Triangle.Acute.svg.png" decoding="async" width="120" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Triangle.Acute.svg/180px-Triangle.Acute.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Triangle.Acute.svg/240px-Triangle.Acute.svg.png 2x" data-file-width="794" data-file-height="491" /></a></span></div> <div class="gallerytext">Triunghi ascuțitunghic. </div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="Drepte,_segmente_și_puncte_remarcabile"><span id="Drepte.2C_segmente_.C8.99i_puncte_remarcabile"></span>Drepte, segmente și puncte remarcabile</h2></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Bissectrices_et_cercle_inscrit.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Bissectrices_et_cercle_inscrit.JPG/250px-Bissectrices_et_cercle_inscrit.JPG" decoding="async" width="250" height="152" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Bissectrices_et_cercle_inscrit.JPG/375px-Bissectrices_et_cercle_inscrit.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/b/bf/Bissectrices_et_cercle_inscrit.JPG 2x" data-file-width="455" data-file-height="277" /></a><figcaption>Bisectoarele interne ale unui triunghi și cercul înscris.</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Triangle_hauteurs.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Triangle_hauteurs.png/250px-Triangle_hauteurs.png" decoding="async" width="250" height="156" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Triangle_hauteurs.png/375px-Triangle_hauteurs.png 1.5x, //upload.wikimedia.org/wikipedia/commons/1/11/Triangle_hauteurs.png 2x" data-file-width="417" data-file-height="260" /></a><figcaption>Înălțimile unui triunghi și ortocentrul.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Bisectoarea">Bisectoarea</h3></div> <p><a href="/wiki/Bisectoare" title="Bisectoare">Bisectoarea</a> este <a href="/wiki/Semidreapt%C4%83" title="Semidreaptă">semidreapta</a> interioară, cu originea în vârful unghiului, care împarte unghiul în 2 unghiuri congruente. Bisectoarele celor trei unghiuri interne ale triunghiului se numesc <i>bisectoarele interne ale triunghiului</i>. </p> <div class="mw-heading mw-heading3"><h3 id="Înălțimea"><span id=".C3.8En.C4.83l.C8.9Bimea"></span>Înălțimea</h3></div> <div role="note" class="dezambiguizare rellink boilerplate seealso">Articol principal: <a href="/wiki/%C3%8En%C4%83l%C8%9Bime_(geometrie)" title="Înălțime (geometrie)">Înălțime (geometrie)</a>.</div><style data-mw-deduplicate="TemplateStyles:r16505893">@media screen{html.skin-theme-clientpref-night .mw-parser-output .rellink{display:flex}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .rellink{display:flex}}</style> <p><a href="/wiki/%C3%8En%C4%83l%C8%9Bime" title="Înălțime">Înălțimea</a> este <a href="/wiki/Segment_de_dreapt%C4%83" class="mw-redirect" title="Segment de dreaptă">segmentul de dreaptă</a> determinat de un vârf al unui triunghi și piciorul perpendicularei duse din acel vârf pe latura opusă sau pe prelungirea ei. </p> <div class="mw-heading mw-heading3"><h3 id="Mediana">Mediana</h3></div> <div role="note" class="dezambiguizare rellink boilerplate seealso">Articol principal: <a href="/wiki/Median%C4%83" title="Mediană">Mediană</a>.</div><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16505893"> <p><a href="/wiki/Mediana" class="mw-redirect" title="Mediana">Mediana</a> este segmentul de dreaptă care unește un vârf al unui triunghi cu mijlocul laturii opuse. </p> <div class="mw-heading mw-heading3"><h3 id="Mediatoarea">Mediatoarea</h3></div> <p><a href="/wiki/Mediatoare" title="Mediatoare">Mediatoarea</a> este dreapta perpendiculară pe un segment dusă prin mijlocul acestuia. Mediatoarele celor trei laturi ale triunghiului se numesc <i>mediatoarele triunghiului</i>. </p> <div class="mw-heading mw-heading3"><h3 id="Linia_mijlocie">Linia mijlocie</h3></div> <div role="note" class="dezambiguizare rellink boilerplate seealso">Articol principal: <a href="/wiki/Linie_mijlocie" title="Linie mijlocie">Linie mijlocie</a>.</div><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16505893"> <p><a href="/wiki/Linia_mijlocie" class="mw-redirect" title="Linia mijlocie">Linia mijlocie</a> este segmentul determinat de mijloacele a două laturi ale triunghiului. Ea este paralelă cu cea de-a treia latură și este egală cu jumătate din lungimea acesteia. Cele trei linii mijlocii ale unui triunghi formează un triunghi asemenea cu triunghiul inițial. </p> <div class="mw-heading mw-heading3"><h3 id="Centrul_cercului_circumscris">Centrul cercului circumscris</h3></div> <p>Centrul <a href="/wiki/Cerc_circumscris" title="Cerc circumscris">cercului circumscris</a> unui triunghi se află la intersecția celor trei <a href="/wiki/Mediatoare" title="Mediatoare">mediatoare</a> (perpendiculare pe mijlocul fiecărei laturi) ale triunghiului respectiv. Centrul cercului circumscris se află în interiorul triunghiului (în cazul triunghiurilor ascuțitunghice) sau în exteriorul triunghiului (în cazul triunghiurilor obtuzunghice). La <a href="/wiki/Triunghi_dreptunghic" title="Triunghi dreptunghic">triunghiurile dreptunghice</a> centrul cercului circumscris se găsește pe <a href="/wiki/Ipotenuz%C4%83" title="Ipotenuză">ipotenuză</a>, la mijlocul acesteia. </p> <div class="mw-heading mw-heading3"><h3 id="Centrul_cercului_înscris"><span id="Centrul_cercului_.C3.AEnscris"></span>Centrul cercului înscris</h3></div> <p>Centrul <a href="/wiki/Cerc" title="Cerc">cercului</a> înscris într-un triunghi se află la intersecția celor trei <a href="/wiki/Bisectoare" title="Bisectoare">bisectoare</a> ale unghiurilor interne ale triunghiului. </p> <div class="mw-heading mw-heading3"><h3 id="Ortocentrul">Ortocentrul</h3></div> <p>Ortocentrul unui triunghi se află la intersecția celor trei <a href="/wiki/%C3%8En%C4%83l%C8%9Bime(geometrie)" class="mw-redirect" title="Înălțime(geometrie)">înălțimi</a> ale triunghiului respectiv. Ortocentrul se află în interiorul triunghiului (în cazul triunghiurilor ascuțitunghice) sau în exteriorul triunghiului (în cazul triunghiurilor obtuzunghice). La <a href="/wiki/Triunghi_dreptunghic" title="Triunghi dreptunghic">triunghiurile dreptunghice</a> ortocentrul este chiar vârful unghiului drept. </p> <div class="mw-heading mw-heading3"><h3 id="Centrul_de_greutate">Centrul de greutate</h3></div> <p>Intersecția celor trei <a href="/wiki/Mediane" class="mw-redirect" title="Mediane">mediane</a> ale triunghiului este „centrul de greutate” al triunghiului. </p><p>Ortocentrul, centrul de greutate și centrul cercului circumscris triunghiului sunt coliniare, formând <i>dreapta lui <a href="/wiki/Euler" class="mw-redirect" title="Euler">Euler</a></i>. </p><p>Centrul de greutate se află pe fiecare mediană la o distanță de 2/3 de la vârf și de 1/3 de la bază. </p> <div class="mw-heading mw-heading2"><h2 id="Congruență"><span id="Congruen.C8.9B.C4.83"></span>Congruență</h2></div> <p>Două triunghiuri sunt congruente dacă <a href="/w/index.php?title=Latur%C4%83&action=edit&redlink=1" class="new" title="Latură — pagină inexistentă">laturile</a> și <a href="/wiki/Unghi" title="Unghi">unghiurile</a> corespunzătoare sunt <a href="/wiki/Congruen%C8%9B%C4%83_(geometrie)" title="Congruență (geometrie)">congruente</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Criterii_de_congruență"><span id="Criterii_de_congruen.C8.9B.C4.83"></span>Criterii de congruență</h3></div> <p>Criteriile de congruență sunt <a href="/wiki/Teorem%C4%83" title="Teoremă">teoreme</a> care permit verificarea congruenței a două triunghiuri folosind numai trei congruențe între elementele lor.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <ol><li>Criteriul U.L.U. (unghi-latură-unghi): Dacă o latură și unghiurile alăturate ei dintr-un triunghi sunt congruente cu elementele corespunzătoare lor din alt triunghi, atunci cele două triunghiuri sunt congruente.</li> <li>Criteriul L.U.L. (latură-unghi-latură): Dacă două laturi și unghiul determinat de ele dintr-un triunghi sunt congruente cu elementele corespunzătoare din alt triunghi, atunci cele 2 triunghiuri sunt congruente.</li> <li>Criteriul L.L.L. (latură-latură-latură): Dacă cele trei laturi dintr-un triunghi sunt congruente cu laturile corespunzătoare lor din alt triunghi, atunci cele două triunghiuri sunt congruente.</li></ol> <div class="mw-heading mw-heading3"><h3 id="Congruența_triunghiurilor_dreptunghice"><span id="Congruen.C8.9Ba_triunghiurilor_dreptunghice"></span>Congruența triunghiurilor dreptunghice</h3></div> <ol><li>Cazul C.C. (catetă-catetă): două triunghiuri dreptunghice care au catetele congruente, sunt congruente.</li> <li>Cazul C.U. (catetă-unghi): două triunghiuri dreptunghice care au câte o catetă și câte un unghi ascuțit congruent,sunt congruente.</li> <li>Cazul I.U. (ipotenuză-unghi): două triunghiuri dreptunghice care au ipotenuzele congruente și o pereche de unghiuri ascuțite congruente, sunt congruente.</li> <li>Cazul I.C. (ipotenuză-catetă): două triunghiuri dreptunghice care au ipotenuzele congruente și o pereche de catete congruente, sunt congruente.</li></ol> <div class="mw-heading mw-heading2"><h2 id="Asemănare"><span id="Asem.C4.83nare"></span>Asemănare</h2></div> <p>Două triunghiuri sunt asemenea dacă au unghiurile corespunzătoare congruente și laturile corespunzătoare proporționale. </p> <div class="mw-heading mw-heading3"><h3 id="Criterii_de_asemănare"><span id="Criterii_de_asem.C4.83nare"></span>Criterii de asemănare</h3></div> <p>Criteriile de asemănare sunt <a href="/wiki/Teorem%C4%83" title="Teoremă">teoreme</a> care permit verificarea asemănării a două triunghiuri.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <ol><li>Criteriul U.U. (unghi-unghi): Două triunghiuri sunt asemenea dacă au câte două unghiuri respectiv congruente .</li> <li>Criteriul L.U.L. (latură-unghi-latura): Dacă două triunghiuri au două laturi proporționale și un unghi congruent, atunci triunghiurile sunt asemenea.</li> <li>Criteriul L.L.L. (latură-latură-latură): Dacă două triunghiuri au laturile corespunzătoare proporționale, atunci cele două triunghiuri sunt asemenea.</li></ol> <div class="mw-heading mw-heading3"><h3 id="Teoreme_și_consecințe"><span id="Teoreme_.C8.99i_consecin.C8.9Be"></span>Teoreme și consecințe</h3></div> <ul><li>O paralelă dusă la una din laturile unui triunghi, formează cu celelalte două laturi, sau cu prelungirile lor, un triunghi asemenea cu triunghiul dat.</li> <li>Orice triunghi este asemenea cu el însuși.</li> <li>Dacă triunghiul ABC este asemenea cu triunghiul A<sub>1</sub>B<sub>1</sub>C<sub>1</sub>, iar triunghiul A<sub>1</sub>B<sub>1</sub>C<sub>1</sub> este asemenea cu triunghiul A<sub>2</sub>B<sub>2</sub>C<sub>2</sub>, atunci și triunghiul ABC este asemenea cu triunghiul A<sub>2</sub>B<sub>2</sub>C<sub>2</sub>.</li> <li>Două triunghiuri congruente sunt întotdeauna asemenea.</li> <li>Toate triunghiurile echilaterale sunt asemenea între ele.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Reguli,_proprietăți,_teoreme_aplicabile"><span id="Reguli.2C_propriet.C4.83.C8.9Bi.2C_teoreme_aplicabile"></span>Reguli, proprietăți, teoreme aplicabile</h2></div> <ol><li>În orice triunghi suma măsurilor unghiurilor interne este de 180°.</li> <li>Un triunghi are șase unghiuri externe, congruente două câte două.</li> <li>Într-un <a href="/wiki/Triunghi_isoscel" title="Triunghi isoscel">triunghi isoscel</a> unghiurile alăturate bazei sunt congruente.</li> <li>Într-un <a href="/wiki/Triunghi_dreptunghic" title="Triunghi dreptunghic">triunghi dreptunghic</a> unghiurile ascuțite sunt complementare.</li> <li>Într-un triunghi dreptunghic lungimea <a href="/wiki/Ipotenuz%C4%83" title="Ipotenuză">ipotenuzei</a> este mai mare decât oricare din lungimile celor două <a href="/wiki/Catet%C4%83" title="Catetă">catete</a>.</li> <li>Într-un triunghi oarecare, laturii mai mari i se opune un unghi mai mare decât cel care se opune laturii mai mici.</li> <li>Într-un triunghi ascuțitunghic centrul cercului circumscris se găsește în interiorul triunghiului.</li> <li>Într-un triunghi obtuzunghic centrul cercului circumscris se găsește în exteriorul triunghiului.</li> <li>Într-un triunghi dreptunghic centrul cercului circumscris coincide cu mijlocul ipotenuzei.</li> <li>Cercul înscris într-un triunghi intersectează (atinge) fiecare latură într-un singur punct, numit punct de tangență.</li> <li>Într-un triunghi se pot construi trei <a href="/wiki/Linie_mijlocie" title="Linie mijlocie">linii mijlocii</a>.</li> <li>Într-un triunghi linia mijlocie este paralelă cu cea de-a treia latură a triunghiului, și are lungimea egală cu jumătate din lungimea acesteia.</li> <li>Triunghiul având ca laturi cele trei linii mijlocii dintr-un triunghi se numește triunghi median.</li> <li>Ortocentrul (punctul de intersecție al celor trei <a href="/wiki/%C3%8En%C4%83l%C8%9Bime_(geometrie)" title="Înălțime (geometrie)">înălțimi</a>) unui triunghi ascuțitunghic se găsește în interiorul triunghiului.</li> <li>Ortocentrul unui triunghi obtuzunghic se găsește în exteriorul triunghiului.</li> <li>Ortocentrul unui triunghi dreptunghic coincide cu vârful unghiului drept.</li> <li><a href="/wiki/Teorema_lui_Thales" title="Teorema lui Thales">Teorema lui Thales</a>: în orice triunghi, o paralelă dusă la una din laturi împarte celelalte două laturi, sau prelungirile acestora, în segmente proporționale.</li> <li><a href="/wiki/Reciproca_Teoremei_lui_Thales" class="mw-redirect" title="Reciproca Teoremei lui Thales">Reciproca Teoremei lui Thales</a>: în orice triunghi, dacă o dreaptă determină pe două laturi, sau pe prelungirile acestora, segmente proporționale, atunci ea este paralelă cu a treia latură.</li> <li><a href="/wiki/Teorema_bisectoarei" title="Teorema bisectoarei">Teorema bisectoarei</a>: bisectoarea unui unghi al unui triunghi oarecare determină pe latura opusă segmente proporționale cu laturile care formează unghiul.</li> <li><a href="/wiki/Teorema_lui_Pitagora" title="Teorema lui Pitagora">Teorema lui Pitagora</a>: într-un triunghi dreptunghic, suma pătratelor lungimilor catetelor este egală cu pătratul lungimii ipotenuzei.</li> <li><a href="/wiki/Teorema_lui_Pitagora_generalizat%C4%83" class="mw-redirect" title="Teorema lui Pitagora generalizată">Teorema lui Pitagora generalizată</a>: într-un triunghi oarecare, pătratul unei laturi este egal cu suma pătratelor celorlalte două laturi minus de două ori produsul lor multiplicat cu cosinusul unghiului dintre ele.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Teorema_lui_Ceva" title="Teorema lui Ceva">Teorema lui Ceva</a>: într-un triunghi oarecare ABC, dacă D, E, F sunt trei puncte diferite de vârfurile triunghiului, aflate respectiv pe laturile acestuia [BC], [CA], [AB], dreptele AD, BE și CF sunt <a href="/wiki/Drepte_concurente" title="Drepte concurente">concurente</a> <a href="/wiki/Dac%C4%83_%C8%99i_numai_dac%C4%83" title="Dacă și numai dacă">dacă și numai dacă</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {DB}{DC}}.{\frac {EC}{EA}}.{\frac {FA}{FB}}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>D</mi> <mi>B</mi> </mrow> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>E</mi> <mi>C</mi> </mrow> <mrow> <mi>E</mi> <mi>A</mi> </mrow> </mfrac> </mrow> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>F</mi> <mi>A</mi> </mrow> <mrow> <mi>F</mi> <mi>B</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {DB}{DC}}.{\frac {EC}{EA}}.{\frac {FA}{FB}}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8818c855a61adb07135b130cff00b436869f945f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:19.575ex; height:5.509ex;" alt="{\displaystyle {\frac {DB}{DC}}.{\frac {EC}{EA}}.{\frac {FA}{FB}}=1}"></span>. <sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li> <li>Teorema lui <a href="/wiki/Ernesto_Ces%C3%A0ro" title="Ernesto Cesàro">Cesàro</a>: într-un triunghi cu laturile <i>a, b, c</i>, are loc relația: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{a}^{4}+m_{a}^{4}+m_{c}^{4}={\tfrac {9}{16}}(a^{4}+b^{4}+c^{4})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>9</mn> <mn>16</mn> </mfrac> </mstyle> </mrow> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{a}^{4}+m_{a}^{4}+m_{c}^{4}={\tfrac {9}{16}}(a^{4}+b^{4}+c^{4})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aca720a0909de97d527ea8960b8e32e237af0ef9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:34.526ex; height:3.676ex;" alt="{\displaystyle m_{a}^{4}+m_{a}^{4}+m_{c}^{4}={\tfrac {9}{16}}(a^{4}+b^{4}+c^{4})}"></span>, unde <i>m<sub>a</sub>, m<sub>b</sub></i> și <i>m<sub>c</sub></i> sunt lungimile medianelor.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></li> <li>Într-un triunghi oarecare, măsura unui unghi exterior triunghiului este egală cu suma măsurilor unghiurilor interioare nealăturate. Un unghi exterior unui triunghi este mai mare decât oricare din unghiurile interne nealăturate.</li></ol> <div class="mw-heading mw-heading2"><h2 id="Formule">Formule</h2></div> <div class="mw-heading mw-heading3"><h3 id="Perimetru_și_semiperimetru"><span id="Perimetru_.C8.99i_semiperimetru"></span>Perimetru și semiperimetru</h3></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{\triangle }=a+b+c\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>+</mo> <mi>c</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\triangle }=a+b+c\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/418de74021636d7da3667c771c94631c9a7c6b80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.38ex; width:15.192ex; height:2.509ex;" alt="{\displaystyle P_{\triangle }=a+b+c\!}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{\triangle }={\frac {P_{\triangle }}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{\triangle }={\frac {P_{\triangle }}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41c1e7c731aec1bbd51951ca49800261943fab9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-left: -0.089ex; width:10.072ex; height:5.343ex;" alt="{\displaystyle p_{\triangle }={\frac {P_{\triangle }}{2}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Arie">Arie</h3></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }\leq {\frac {P_{\triangle }^{2}}{12{\sqrt {3}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>≤</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mrow> <mn>12</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }\leq {\frac {P_{\triangle }^{2}}{12{\sqrt {3}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e2907159d866f36ab9434f4c28333fcaad92f3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:12.794ex; height:7.009ex;" alt="{\displaystyle A_{\triangle }\leq {\frac {P_{\triangle }^{2}}{12{\sqrt {3}}}}}"></span>, iar <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle ec}={\frac {P_{\triangle }^{2}}{12{\sqrt {3}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> <mi>e</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mrow> <mn>12</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle ec}={\frac {P_{\triangle }^{2}}{12{\sqrt {3}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/378790917b21328b357e8f9b0ba5b3abf588cfb1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.272ex; height:7.009ex;" alt="{\displaystyle A_{\triangle ec}={\frac {P_{\triangle }^{2}}{12{\sqrt {3}}}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }={\frac {l\cdot h_{l}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>l</mi> <mo>⋅</mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }={\frac {l\cdot h_{l}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb8984ceffc59136ca927644f7448adc2f97f42d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.805ex; height:5.343ex;" alt="{\displaystyle A_{\triangle }={\frac {l\cdot h_{l}}{2}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle dr}={\frac {1}{2}}b*c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>b</mi> <mo>∗</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle dr}={\frac {1}{2}}b*c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df02cc8a1f247763085495f807ec4e18ebd94a50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.334ex; height:5.176ex;" alt="{\displaystyle A_{\triangle dr}={\frac {1}{2}}b*c}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle ec}={\frac {l^{2}{\sqrt {3}}}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> <mi>e</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mrow> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle ec}={\frac {l^{2}{\sqrt {3}}}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07f8af0768ace1a543e61b961ee3acec7560ef47" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.695ex; height:5.843ex;" alt="{\displaystyle A_{\triangle ec}={\frac {l^{2}{\sqrt {3}}}{4}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }=pr}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <mi>p</mi> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }=pr}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6c50df662c946c0502a8d672de602841a19e6c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.753ex; height:2.509ex;" alt="{\displaystyle A_{\triangle }=pr}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }={\frac {abc}{4R}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> <mrow> <mn>4</mn> <mi>R</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }={\frac {abc}{4R}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b83c0561a95cc5d3a2e011483c4098d121814ff6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.605ex; height:5.509ex;" alt="{\displaystyle A_{\triangle }={\frac {abc}{4R}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }={\frac {D^{2}\cdot \sin \alpha \cdot \sin \beta \cdot \sin \gamma }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mi>γ</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }={\frac {D^{2}\cdot \sin \alpha \cdot \sin \beta \cdot \sin \gamma }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c2f68449d011e009e368de2edfeaa1f90d9b2b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:29.197ex; height:5.676ex;" alt="{\displaystyle A_{\triangle }={\frac {D^{2}\cdot \sin \alpha \cdot \sin \beta \cdot \sin \gamma }{2}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }={\frac {ab\cdot \sin(a;b)}{2}}={\frac {bc\cdot \sin(b;c)}{2}}={\frac {ac\cdot \sin(a;c)}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mi>b</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>;</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>b</mi> <mi>c</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo>;</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mi>c</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>;</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }={\frac {ab\cdot \sin(a;b)}{2}}={\frac {bc\cdot \sin(b;c)}{2}}={\frac {ac\cdot \sin(a;c)}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/598daa814141e650355eabcaee3bb96c6232ef99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:50.311ex; height:5.676ex;" alt="{\displaystyle A_{\triangle }={\frac {ab\cdot \sin(a;b)}{2}}={\frac {bc\cdot \sin(b;c)}{2}}={\frac {ac\cdot \sin(a;c)}{2}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }={\frac {\sqrt {ab\cdot h_{a}h_{b}}}{2}}={\frac {\sqrt {ac\cdot h_{a}h_{c}}}{2}}={\frac {\sqrt {bc\cdot h_{b}h_{c}}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mi>a</mi> <mi>b</mi> <mo>⋅</mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </msqrt> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mi>a</mi> <mi>c</mi> <mo>⋅</mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </msqrt> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mi>b</mi> <mi>c</mi> <mo>⋅</mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </msqrt> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }={\frac {\sqrt {ab\cdot h_{a}h_{b}}}{2}}={\frac {\sqrt {ac\cdot h_{a}h_{c}}}{2}}={\frac {\sqrt {bc\cdot h_{b}h_{c}}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/710fae17a13360c2f4f6bc7cb41b66e5e8885d25" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:47.718ex; height:6.176ex;" alt="{\displaystyle A_{\triangle }={\frac {\sqrt {ab\cdot h_{a}h_{b}}}{2}}={\frac {\sqrt {ac\cdot h_{a}h_{c}}}{2}}={\frac {\sqrt {bc\cdot h_{b}h_{c}}}{2}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }={\frac {a+b}{2(h_{a}^{-1}+h_{b}^{-1})}}={\frac {a+c}{2(h_{a}^{-1}+h_{c}^{-1})}}={\frac {b+c}{2(h_{b}^{-1}+h_{c}^{-1})}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mo>+</mo> <mi>b</mi> </mrow> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mo>+</mo> <mi>c</mi> </mrow> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>b</mi> <mo>+</mo> <mi>c</mi> </mrow> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }={\frac {a+b}{2(h_{a}^{-1}+h_{b}^{-1})}}={\frac {a+c}{2(h_{a}^{-1}+h_{c}^{-1})}}={\frac {b+c}{2(h_{b}^{-1}+h_{c}^{-1})}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6973a5367c3d664c3f9380d03d7afb5708c6e75a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:54.707ex; height:6.676ex;" alt="{\displaystyle A_{\triangle }={\frac {a+b}{2(h_{a}^{-1}+h_{b}^{-1})}}={\frac {a+c}{2(h_{a}^{-1}+h_{c}^{-1})}}={\frac {b+c}{2(h_{b}^{-1}+h_{c}^{-1})}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }={\frac {Rh_{b}h_{c}}{a}}={\frac {Rh_{a}h_{c}}{b}}={\frac {Rh_{a}h_{b}}{c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>R</mi> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mrow> <mi>a</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>R</mi> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mrow> <mi>b</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>R</mi> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mrow> <mi>c</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }={\frac {Rh_{b}h_{c}}{a}}={\frac {Rh_{a}h_{c}}{b}}={\frac {Rh_{a}h_{b}}{c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29b74c9f0689c11588a4f6af235e30a05ce362c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:34.533ex; height:5.509ex;" alt="{\displaystyle A_{\triangle }={\frac {Rh_{b}h_{c}}{a}}={\frac {Rh_{a}h_{c}}{b}}={\frac {Rh_{a}h_{b}}{c}}}"></span></dd></dl> <p><b>Formula lui Heron:</b> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }={\frac {\sqrt {P(a-b+c)(a+b-c)(-a+b+c)}}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mi>P</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>b</mi> <mo>+</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>+</mo> <mi>c</mi> <mo stretchy="false">)</mo> </msqrt> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }={\frac {\sqrt {P(a-b+c)(a+b-c)(-a+b+c)}}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc251f244d858176c0f74120f55097a57523dd16" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:45.421ex; height:6.176ex;" alt="{\displaystyle A_{\triangle }={\frac {\sqrt {P(a-b+c)(a+b-c)(-a+b+c)}}{4}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }={\sqrt {p(p-a)(p-b)(p-c)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>p</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo>−</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>p</mi> <mo>−</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>p</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }={\sqrt {p(p-a)(p-b)(p-c)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9cd699756b0eb1cef4d28727f5954213d964a6c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:30.719ex; height:4.843ex;" alt="{\displaystyle A_{\triangle }={\sqrt {p(p-a)(p-b)(p-c)}}}"></span></dd></dl> <p><b>Alte forme ale formulei lui Heron:</b> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }={\frac {\sqrt {(a^{2}+b^{2}+c^{2})^{2}-2(a^{4}+b^{4}+c^{4})}}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo stretchy="false">)</mo> </msqrt> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }={\frac {\sqrt {(a^{2}+b^{2}+c^{2})^{2}-2(a^{4}+b^{4}+c^{4})}}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6192f48fad47873e39c32da1b771d25a740875c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:42.526ex; height:6.176ex;" alt="{\displaystyle A_{\triangle }={\frac {\sqrt {(a^{2}+b^{2}+c^{2})^{2}-2(a^{4}+b^{4}+c^{4})}}{4}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }={\frac {\sqrt {2(a^{2}b^{2}+a^{2}c^{2}+b^{2}c^{2})-(a^{4}+b^{4}+c^{4})}}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>2</mn> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>−</mo> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo stretchy="false">)</mo> </msqrt> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }={\frac {\sqrt {2(a^{2}b^{2}+a^{2}c^{2}+b^{2}c^{2})-(a^{4}+b^{4}+c^{4})}}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee5eae2675873896f85e870d6af0c60b3c87c1b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:47.868ex; height:6.176ex;" alt="{\displaystyle A_{\triangle }={\frac {\sqrt {2(a^{2}b^{2}+a^{2}c^{2}+b^{2}c^{2})-(a^{4}+b^{4}+c^{4})}}{4}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }={\frac {\sqrt {(a+b-c)(a-b+c)(-a+b+c)(a+b+c)}}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>b</mi> <mo>+</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>+</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>+</mo> <mi>c</mi> <mo stretchy="false">)</mo> </msqrt> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }={\frac {\sqrt {(a+b-c)(a-b+c)(-a+b+c)(a+b+c)}}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c463413d1f70e85585bc2a070d8b4a77427b9028" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:54.4ex; height:6.176ex;" alt="{\displaystyle A_{\triangle }={\frac {\sqrt {(a+b-c)(a-b+c)(-a+b+c)(a+b+c)}}{4}}}"></span></dd></dl> <p><b>Formule derivate din formula lui Heron:</b> </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Triangle_with_notations_2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Triangle_with_notations_2.svg/220px-Triangle_with_notations_2.svg.png" decoding="async" width="220" height="131" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Triangle_with_notations_2.svg/330px-Triangle_with_notations_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/49/Triangle_with_notations_2.svg/440px-Triangle_with_notations_2.svg.png 2x" data-file-width="790" data-file-height="469" /></a><figcaption>Un triunghi cu laturile de lungime a, b și respectiv c și unghiurile de măsura α, β și respectiv γ.</figcaption></figure> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }={\frac {4{\sqrt {\sigma (\sigma -m_{a})(\sigma -m_{b})(\sigma -m_{c})}}}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>σ</mi> <mo stretchy="false">(</mo> <mi>σ</mi> <mo>−</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>σ</mi> <mo>−</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>σ</mi> <mo>−</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo stretchy="false">)</mo> </msqrt> </mrow> </mrow> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }={\frac {4{\sqrt {\sigma (\sigma -m_{a})(\sigma -m_{b})(\sigma -m_{c})}}}{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac05f1a74ea718ea7101cdb3375c22be7a3ef9dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:39.23ex; height:6.176ex;" alt="{\displaystyle A_{\triangle }={\frac {4{\sqrt {\sigma (\sigma -m_{a})(\sigma -m_{b})(\sigma -m_{c})}}}{3}}}"></span></dd> <dd>unde</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma ={\frac {m_{a}+m_{b}+m_{c}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma ={\frac {m_{a}+m_{b}+m_{c}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51d4031ecfd5b8e1b3d174a000dcbce1acc63aea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:20.05ex; height:5.009ex;" alt="{\displaystyle \sigma ={\frac {m_{a}+m_{b}+m_{c}}{2}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }^{-1}=4{\sqrt {H(H-h_{a}^{-1})(H-h_{b}^{-1})(H-h_{c}^{-1})}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>H</mi> <mo stretchy="false">(</mo> <mi>H</mi> <mo>−</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>H</mi> <mo>−</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>H</mi> <mo>−</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> <mo stretchy="false">)</mo> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }^{-1}=4{\sqrt {H(H-h_{a}^{-1})(H-h_{b}^{-1})(H-h_{c}^{-1})}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b2395c65a16d90486a0831e117bab1b3f9ba39f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:43.879ex; height:4.843ex;" alt="{\displaystyle A_{\triangle }^{-1}=4{\sqrt {H(H-h_{a}^{-1})(H-h_{b}^{-1})(H-h_{c}^{-1})}}}"></span></dd> <dd>unde</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H={\frac {h_{a}^{-1}+h_{b}^{-1}+h_{c}^{-1}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H={\frac {h_{a}^{-1}+h_{b}^{-1}+h_{c}^{-1}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f4378163feb9498185d750f485b4f068b4dbaa0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:22.694ex; height:6.176ex;" alt="{\displaystyle H={\frac {h_{a}^{-1}+h_{b}^{-1}+h_{c}^{-1}}{2}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{\triangle }=D^{2}{\sqrt {S(S-\sin \alpha )(S-\sin \beta )(S-\sin \gamma )}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> <mo>=</mo> <msup> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>S</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>S</mi> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>S</mi> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{\triangle }=D^{2}{\sqrt {S(S-\sin \alpha )(S-\sin \beta )(S-\sin \gamma )}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c59a298c2edd4f2c9e364a32702d2e7cde92fdc0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:45.593ex; height:4.843ex;" alt="{\displaystyle A_{\triangle }=D^{2}{\sqrt {S(S-\sin \alpha )(S-\sin \beta )(S-\sin \gamma )}}}"></span></dd> <dd>unde <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S={\frac {\sin \alpha +\sin \beta +\sin \gamma }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo>+</mo> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> <mo>+</mo> <mi>sin</mi> <mo>⁡</mo> <mi>γ</mi> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S={\frac {\sin \alpha +\sin \beta +\sin \gamma }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3050ba6e4f02a84c5eeb8806f48853315942bcc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:24.925ex; height:5.509ex;" alt="{\displaystyle S={\frac {\sin \alpha +\sin \beta +\sin \gamma }{2}}}"></span>, iar<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D={\frac {a}{\sin \alpha }}={\frac {b}{\sin \beta }}={\frac {c}{\sin \gamma }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>b</mi> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>γ</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D={\frac {a}{\sin \alpha }}={\frac {b}{\sin \beta }}={\frac {c}{\sin \gamma }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7fe5d96ec521c67195cf7709fa4ed93a3492e53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:27.538ex; height:5.843ex;" alt="{\displaystyle D={\frac {a}{\sin \alpha }}={\frac {b}{\sin \beta }}={\frac {c}{\sin \gamma }}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Alte_formule">Alte formule</h3></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{\triangle ec}={\frac {l{\sqrt {3}}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> <mi>e</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{\triangle ec}={\frac {l{\sqrt {3}}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9afaf9c93e150bd98f2c5a08f8ea84686e881de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.236ex; height:5.843ex;" alt="{\displaystyle h_{\triangle ec}={\frac {l{\sqrt {3}}}{2}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{\triangle dr}={\frac {xy}{i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mi>y</mi> </mrow> <mi>i</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{\triangle dr}={\frac {xy}{i}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cc3944c56ea1495a8b3f412f70714a064ffe8ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.053ex; height:4.843ex;" alt="{\displaystyle h_{\triangle dr}={\frac {xy}{i}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{\triangle dr}={\sqrt {pr_{x}\cdot pr_{y}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>p</mi> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>⋅</mo> <mi>p</mi> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{\triangle dr}={\sqrt {pr_{x}\cdot pr_{y}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0d55816267368989b056af86f81b582d300684c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:18.005ex; height:3.176ex;" alt="{\displaystyle h_{\triangle dr}={\sqrt {pr_{x}\cdot pr_{y}}}}"></span> sau <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{\triangle dr}^{2}=pr_{x}\cdot pr_{y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> <mi>d</mi> <mi>r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <mi>p</mi> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>⋅</mo> <mi>p</mi> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{\triangle dr}^{2}=pr_{x}\cdot pr_{y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545c12d85d4222abddc1b637870f8601fa204a17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:16.069ex; height:3.176ex;" alt="{\displaystyle h_{\triangle dr}^{2}=pr_{x}\cdot pr_{y}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{\triangle dr}\cdot i=xy}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> <mi>d</mi> <mi>r</mi> </mrow> </msub> <mo>⋅</mo> <mi>i</mi> <mo>=</mo> <mi>x</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{\triangle dr}\cdot i=xy}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80720cf3852e8db7894997914f77405455dc43e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.699ex; height:2.509ex;" alt="{\displaystyle h_{\triangle dr}\cdot i=xy}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i^{2}=x^{2}+y^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i^{2}=x^{2}+y^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ecebafe1fff1dce1bc5db80ad38caf4dc3ed8825" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.781ex; height:3.009ex;" alt="{\displaystyle i^{2}=x^{2}+y^{2}\,}"></span> sau <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i={\sqrt {x^{2}+y^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i={\sqrt {x^{2}+y^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75d5f8eac15728dbbf02a91fe574e269e0f07b5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:13.664ex; height:4.843ex;" alt="{\displaystyle i={\sqrt {x^{2}+y^{2}}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c={\sqrt {pr_{c}\cdot i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>p</mi> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>⋅</mo> <mi>i</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c={\sqrt {pr_{c}\cdot i}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/053d3cc1dcaa21d1654044e41eb1d09229ca2dd4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:12.073ex; height:3.509ex;" alt="{\displaystyle c={\sqrt {pr_{c}\cdot i}}}"></span> sau <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c^{2}=pr_{c}\cdot i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>p</mi> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>⋅</mo> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c^{2}=pr_{c}\cdot i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc25311e6f80fd721a80715b7e90f9c86a5d712d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.803ex; height:3.009ex;" alt="{\displaystyle c^{2}=pr_{c}\cdot i}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{i}={\frac {i}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>i</mi> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{i}={\frac {i}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52728ea8519b1ec1709fde493aa9e2aea50210b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.937ex; height:5.176ex;" alt="{\displaystyle m_{i}={\frac {i}{2}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{a}={\frac {\sqrt {2b^{2}+2c^{2}-a^{2}}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>2</mn> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{a}={\frac {\sqrt {2b^{2}+2c^{2}-a^{2}}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a03e996895d1f2b4c04d3cfb80684b2c3dd4475c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:23.803ex; height:6.176ex;" alt="{\displaystyle m_{a}={\frac {\sqrt {2b^{2}+2c^{2}-a^{2}}}{2}}}"></span> ; <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{b}={\frac {\sqrt {2a^{2}+2c^{2}-b^{2}}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>2</mn> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{b}={\frac {\sqrt {2a^{2}+2c^{2}-b^{2}}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15c5d6577fe36ce9d564abe3742c39bf10b999e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:23.639ex; height:6.176ex;" alt="{\displaystyle m_{b}={\frac {\sqrt {2a^{2}+2c^{2}-b^{2}}}{2}}}"></span> ; <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{c}={\frac {\sqrt {2a^{2}+2b^{2}-c^{2}}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>2</mn> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{c}={\frac {\sqrt {2a^{2}+2b^{2}-c^{2}}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d87e31f69f7ec283c55a436961d196c974edafa5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:23.646ex; height:6.176ex;" alt="{\displaystyle m_{c}={\frac {\sqrt {2a^{2}+2b^{2}-c^{2}}}{2}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{a}={\sqrt {{\frac {a^{2}+b^{2}+c^{2}}{2}}-{\frac {3a^{2}}{4}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>4</mn> </mfrac> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{a}={\sqrt {{\frac {a^{2}+b^{2}+c^{2}}{2}}-{\frac {3a^{2}}{4}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c6b30b75a953edf08c5b944970c113ca8aadd72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:28.601ex; height:6.176ex;" alt="{\displaystyle m_{a}={\sqrt {{\frac {a^{2}+b^{2}+c^{2}}{2}}-{\frac {3a^{2}}{4}}}}}"></span> ; <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{b}={\sqrt {{\frac {a^{2}+b^{2}+c^{2}}{2}}-{\frac {3b^{2}}{4}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>4</mn> </mfrac> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{b}={\sqrt {{\frac {a^{2}+b^{2}+c^{2}}{2}}-{\frac {3b^{2}}{4}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b21f7c870413eda2feedc43c72ce99c3bbf096a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:28.205ex; height:6.176ex;" alt="{\displaystyle m_{b}={\sqrt {{\frac {a^{2}+b^{2}+c^{2}}{2}}-{\frac {3b^{2}}{4}}}}}"></span> ; <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{c}={\sqrt {{\frac {a^{2}+b^{2}+c^{2}}{2}}-{\frac {3c^{2}}{4}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>4</mn> </mfrac> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{c}={\sqrt {{\frac {a^{2}+b^{2}+c^{2}}{2}}-{\frac {3c^{2}}{4}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/293534efddcd63252f034325070a02daaf621d37" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:28.221ex; height:6.176ex;" alt="{\displaystyle m_{c}={\sqrt {{\frac {a^{2}+b^{2}+c^{2}}{2}}-{\frac {3c^{2}}{4}}}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\triangle ec}={\frac {l{\sqrt {3}}}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> <mi>e</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mrow> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\triangle ec}={\frac {l{\sqrt {3}}}{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03753d45f137afcab14e4b9465c723c60046f48f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.661ex; height:5.843ex;" alt="{\displaystyle R_{\triangle ec}={\frac {l{\sqrt {3}}}{3}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{\triangle ec}={\frac {l{\sqrt {3}}}{6}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> <mi>e</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mrow> <mn>6</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{\triangle ec}={\frac {l{\sqrt {3}}}{6}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42ea565485fe1ef5997742565d89500f570f43ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.946ex; height:5.843ex;" alt="{\displaystyle r_{\triangle ec}={\frac {l{\sqrt {3}}}{6}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r={\frac {2A_{\triangle }}{P_{\triangle }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> </mrow> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\frac {2A_{\triangle }}{P_{\triangle }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3282f9a1750350b4a8057d2accb8ce6246e2729a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:9.582ex; height:5.843ex;" alt="{\displaystyle r={\frac {2A_{\triangle }}{P_{\triangle }}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r={\sqrt {\frac {(p-a)(p-b)(p-c)}{p}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>−</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>p</mi> <mo>−</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>p</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> <mi>p</mi> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\sqrt {\frac {(p-a)(p-b)(p-c)}{p}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb30b98f161fff2aea1a210eb76b5aa5d28ac34b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:27.999ex; height:7.509ex;" alt="{\displaystyle r={\sqrt {\frac {(p-a)(p-b)(p-c)}{p}}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {3(a^{2}+b^{2}+c^{2})}{4}}=m_{a}^{2}+m_{b}^{2}+m_{c}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mn>4</mn> </mfrac> </mrow> <mo>=</mo> <msubsup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {3(a^{2}+b^{2}+c^{2})}{4}}=m_{a}^{2}+m_{b}^{2}+m_{c}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/94c5c4873c47bc7ea9639f7faa92541db7102f52" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:33.996ex; height:5.843ex;" alt="{\displaystyle {\frac {3(a^{2}+b^{2}+c^{2})}{4}}=m_{a}^{2}+m_{b}^{2}+m_{c}^{2}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{r}}={\frac {1}{h_{a}}}+{\frac {1}{h_{b}}}+{\frac {1}{h_{c}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>r</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{r}}={\frac {1}{h_{a}}}+{\frac {1}{h_{b}}}+{\frac {1}{h_{c}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/053bcbf085e893a90fa9ba0a6ace801b1bbd6d48" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:20.287ex; height:5.676ex;" alt="{\displaystyle {\frac {1}{r}}={\frac {1}{h_{a}}}+{\frac {1}{h_{b}}}+{\frac {1}{h_{c}}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {r}{R}}={\frac {4A_{\triangle }^{2}}{p\cdot abc}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>r</mi> <mi>R</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <msubsup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">△</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mrow> <mi>p</mi> <mo>⋅</mo> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {r}{R}}={\frac {4A_{\triangle }^{2}}{p\cdot abc}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3a12e862deea6f6e13ed7775daf6a7cc6721e39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.617ex; height:6.509ex;" alt="{\displaystyle {\frac {r}{R}}={\frac {4A_{\triangle }^{2}}{p\cdot abc}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {r}{R}}=\cos \alpha +\cos \beta +\cos \gamma -1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>r</mi> <mi>R</mi> </mfrac> </mrow> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mi>γ</mi> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {r}{R}}=\cos \alpha +\cos \beta +\cos \gamma -1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/663312e1c652eb1335ba1cef9e9addc5b20b568d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:29.959ex; height:4.843ex;" alt="{\displaystyle {\frac {r}{R}}=\cos \alpha +\cos \beta +\cos \gamma -1}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2Rr={\frac {abc}{a+b+c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>R</mi> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> <mrow> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>+</mo> <mi>c</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2Rr={\frac {abc}{a+b+c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/663e37165bc07debf90f77989138647fd781e288" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:16.825ex; height:5.676ex;" alt="{\displaystyle 2Rr={\frac {abc}{a+b+c}}}"></span></dd></dl> <p><i>Notă</i>. Au fost utilizate notațiile: </p><p><i>A</i> (arie); <i>l</i> (una dintre laturile triunghiului); <i>a, b, c</i> (laturile unui triunghi); α,β,γ (unghiurile triunghiului); <i>P</i> (perimetru); <i>p</i> (semiperimetru); <i>h</i> (înălțime); <i>R</i> (raza cercului circumscris triunghiului); <i>D</i> (diametrul cercului circumscris al triunghiului) ; <i>r</i> (raza cercului înscris în triunghi); <i>pr</i> (proiecția catetei pe ipotenuză); <i>m</i> (mediana). </p> <div class="mw-heading mw-heading2"><h2 id="Note">Note</h2></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><b><a href="#cite_ref-1">^</a></b> <span class="reference-text">Hadamard (1962), <i>Lecții de geometrie elementară. Geometrie plană</i>, p. 28.</span> </li> <li id="cite_note-2"><b><a href="#cite_ref-2">^</a></b> <span class="reference-text">Hadamard (1962), <i>Lecții de geometrie elementară. Geometrie plană</i>, p. 93.</span> </li> <li id="cite_note-3"><b><a href="#cite_ref-3">^</a></b> <span class="reference-text"><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba franceză">fr</span> W. Gellert, H. Küstner, M. Hellwich, H. Kästner, <i>Petite encyclopédie des mathématiques</i>, Édition Didier, Paris, 1980, chapitre 11-2, p. 265. <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/9782278035267" class="internal mw-magiclink-isbn">ISBN 978-2-278-03526-7</a></span> </li> <li id="cite_note-4"><b><a href="#cite_ref-4">^</a></b> <span class="reference-text">Viorel Gh. Vodă (1983), <i>Vraja geometriei demodate</i>, p. 226.</span> </li> <li id="cite_note-5"><b><a href="#cite_ref-5">^</a></b> <span class="reference-text">Viorel Gh. Vodă (1983), <i>Vraja geometriei demodate</i>, p. 225.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografie">Bibliografie</h2></div> <ul><li><a href="/wiki/Jacques_Hadamard" title="Jacques Hadamard">Jacques Hadamard</a>, <i>Lecții de geometrie elementară. Geometrie plană</i>, Editura Tehnică, București, 1962</li> <li>Viorel Gh. Vodă, <i>Vraja geometriei demodate</i>, Editura Albatros, București, 1983</li> <li>Dumitru Săvulescu, Ștefan Sabău, Emil Teodorescu. <i>Breviar teoretic și teste de matematică</i>, Editura Corint, București 2001.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Lectură_suplimentară"><span id="Lectur.C4.83_suplimentar.C4.83"></span>Lectură suplimentară</h2></div> <ul><li><a href="/wiki/Traian_Lalescu" title="Traian Lalescu">Traian Lalescu</a>, <i>Geometria triunghiului</i>, Editura Tineretului, București, 1958.</li> <li>Ionescu-Țiu, C., <i>Geometrie plană și în spațiu, pentru admiterea la facultate</i>, Editura Albatros, București, 1976.</li> <li>Cătălin Barbu, <i>Teoreme fundamentale din geometria triunghiului</i>, Editura Unique, 2008.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Legături_externe"><span id="Leg.C4.83turi_externe"></span>Legături externe</h2></div> <div class="noprint" style="clear: right; border: solid #aaa 1px; margin: 0 0 1em 1em; font-size: 90%; background: #f9f9f9; width: 230px; padding: 2px; spacing: 2px; text-align: center; float: right;"> <div style="float: left;"><figure class="mw-halign-none" typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Wiktionary-logo.svg" class="mw-file-description" title="Wikţionar"><img alt="Wikţionar" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/30px-Wiktionary-logo.svg.png" decoding="async" width="30" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/45px-Wiktionary-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/60px-Wiktionary-logo.svg.png 2x" data-file-width="370" data-file-height="350" /></a><figcaption>Wikţionar</figcaption></figure></div> <div style="margin-left: 35px; line-height:normal;">Caută „<b><a href="https://ro.wiktionary.org/wiki/triunghi" class="extiw" title="wikt:triunghi">triunghi</a></b>” în <a href="/wiki/Wik%C8%9Bionar" title="Wikționar">Wikționar</a>, dicționarul liber.</div> </div> <p><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Commons-logo.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Materiale media legate de <span class="plainlinks"><b><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Triangles?uselang=ro">triunghi</a></b></span> la <a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons">Wikimedia Commons</a> </p> <ul><li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/Triangle.html">Wolfram MathWorld: Triangle</a>, accesat la 9 octombrie 2020</li></ul> <div role="navigation" class="navbox" aria-labelledby="Poligoane" style="padding:3px"><table class="nowraplinks collapsible autocollapse navbox-inner" style="border-spacing:0;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div class="plainlinks hlist navbar mini"><ul><li class="nv-view"><a href="/wiki/Format:Poligoane" title="Format:Poligoane"><abbr title="Vizualizează acest format" style=";;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none;">v</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=Discu%C8%9Bie_Format:Poligoane&action=edit&redlink=1" class="new" title="Discuție Format:Poligoane — pagină inexistentă"><abbr title="Discută acest format" style=";;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none;">d</abbr></a></li><li class="nv-edit"><a class="external text" href="https://ro.wikipedia.org/w/index.php?title=Format:Poligoane&action=edit"><abbr title="Modifică acest format" style=";;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none;">m</abbr></a></li></ul></div><div id="Poligoane" style="font-size:100%;margin:0 4em"><a href="/wiki/Poligon" title="Poligon">Poligoane</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">Triunghiuri</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Triunghi_ascu%C8%9Bitunghic" class="mw-redirect" title="Triunghi ascuțitunghic">Ascuțitunghic</a> <ul><li><a href="/wiki/Triunghi_de_aur" title="Triunghi de aur">de aur</a></li></ul></li> <li><a href="/wiki/Triunghi_dreptunghic" title="Triunghi dreptunghic">Dreptunghic</a></li> <li><a href="/wiki/Triunghi_echilateral" title="Triunghi echilateral">Echilateral</a></li> <li><a href="/wiki/Triunghi_hiperbolic#Triunghi_ideal" title="Triunghi hiperbolic">Ideal</a></li> <li><a href="/wiki/Triunghi_isoscel" title="Triunghi isoscel">Isoscel</a></li> <li><a href="/wiki/Triunghi_obtuzunghic" class="mw-redirect" title="Triunghi obtuzunghic">Obtuzunghic</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Patrulater" title="Patrulater">Patrulatere</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Antiparalelogram" title="Antiparalelogram">Antiparalelogram</a></li> <li><a href="/wiki/Patrulater_armonic" title="Patrulater armonic">Armonic</a></li> <li><a href="/wiki/Patrulater_bicentric" title="Patrulater bicentric">Bicentric</a></li> <li><a href="/wiki/Patrulater_circumscriptibil" title="Patrulater circumscriptibil">Circumscriptibil</a></li> <li><a href="/wiki/Dreptunghi" title="Dreptunghi">Dreptunghi</a> <ul><li><a href="/wiki/Dreptunghi_de_aur" title="Dreptunghi de aur">de aur</a></li></ul></li> <li><a href="/wiki/Patrulater_echidiagonal" title="Patrulater echidiagonal">Echidiagonal</a></li> <li><a href="/wiki/Patrulater_exscriptibil" title="Patrulater exscriptibil">Exscriptibil</a></li> <li><a href="/wiki/Patrulater_inscriptibil" title="Patrulater inscriptibil">Inscriptibil</a></li> <li><a href="/wiki/Patrulater_Lambert" title="Patrulater Lambert">Lambert</a></li> <li><a href="/wiki/Patrulater_ortodiagonal" title="Patrulater ortodiagonal">Ortodiagonal</a></li> <li><a href="/wiki/Paralelogram" title="Paralelogram">Paralelogram</a></li> <li><a href="/wiki/P%C4%83trat" title="Pătrat">Pătrat</a></li> <li><a href="/wiki/Romb" title="Romb">Romb</a> <ul><li><a href="/wiki/Romb_de_aur" title="Romb de aur">de aur</a></li></ul></li> <li><a href="/wiki/Romboid" title="Romboid">Romboid</a> <ul><li><a href="/wiki/Romboid_dreptunghic" title="Romboid dreptunghic">dreptunghic</a></li></ul></li> <li><a href="/wiki/Patrulater_Saccheri" title="Patrulater Saccheri">Saccheri</a></li> <li><a href="/wiki/Trapez" title="Trapez">Trapez</a> <ul><li><a href="/wiki/Trapez_isoscel" class="mw-redirect" title="Trapez isoscel">isoscel</a></li> <li><a href="/wiki/Trapez_circumscriptibil" title="Trapez circumscriptibil">circumscriptibil</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">După numărul de laturi</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Monogon" title="Monogon">Monogon (1)</a></li> <li><a href="/wiki/Digon" title="Digon">Digon (2)</a></li> <li><a class="mw-selflink selflink">Triunghi (3)</a></li> <li><a href="/wiki/Patrulater" title="Patrulater">Patrulater (4)</a></li> <li><a href="/wiki/Pentagon" title="Pentagon">Pentagon (5)</a></li> <li><a href="/wiki/Hexagon" title="Hexagon">Hexagon (6)</a></li> <li><a href="/wiki/Heptagon" title="Heptagon">Heptagon (7)</a></li> <li><a href="/wiki/Octogon" title="Octogon">Octogon (8)</a></li> <li><a href="/wiki/Eneagon" title="Eneagon">Eneagon (9)</a></li> <li><a href="/wiki/Decagon" title="Decagon">Decagon (10)</a></li> <li><a href="/wiki/Endecagon" title="Endecagon">Endecagon (11)</a></li> <li><a href="/wiki/Dodecagon" title="Dodecagon">Dodecagon (12)</a></li> <li><a href="/wiki/Tridecagon" title="Tridecagon">Tridecagon (13)</a></li> <li><a href="/wiki/Tetradecagon" title="Tetradecagon">Tetradecagon (14)</a></li> <li><a href="/wiki/Pentadecagon" title="Pentadecagon">Pentadecagon (15)</a></li> <li><a href="/wiki/Hexadecagon" title="Hexadecagon">Hexadecagon (16)</a></li> <li><a href="/wiki/Heptadecagon" title="Heptadecagon">Heptadecagon (17)</a></li> <li><a href="/wiki/Octodecagon" title="Octodecagon">Octodecagon (18)</a></li> <li><a href="/wiki/Eneadecagon" title="Eneadecagon">Eneadecagon (19)</a></li> <li><a href="/wiki/Icosagon" title="Icosagon">Icosagon (20)</a></li> <li><a href="/wiki/Icosidigon" title="Icosidigon">Icosidigon (22)</a></li> <li><a href="/wiki/Triacontagon" title="Triacontagon">Triacontagon (30)</a></li> <li><a href="/wiki/Tetracontagon" title="Tetracontagon">Tetracontagon (40)</a></li> <li><a href="/w/index.php?title=Pentacontagon&action=edit&redlink=1" class="new" title="Pentacontagon — pagină inexistentă">Pentacontagon (50)</a></li> <li><a href="/w/index.php?title=Hexacontagon&action=edit&redlink=1" class="new" title="Hexacontagon — pagină inexistentă">Hexacontagon (60)</a></li> <li><a href="/w/index.php?title=Heptacontagon&action=edit&redlink=1" class="new" title="Heptacontagon — pagină inexistentă">Heptacontagon (70)</a></li> <li><a href="/w/index.php?title=Octocontagon&action=edit&redlink=1" class="new" title="Octocontagon — pagină inexistentă">Octocontagon (80)</a></li> <li><a href="/w/index.php?title=Eneacontagon&action=edit&redlink=1" class="new" title="Eneacontagon — pagină inexistentă">Eneacontagon (90)</a></li> <li><a href="/w/index.php?title=Hectogon&action=edit&redlink=1" class="new" title="Hectogon — pagină inexistentă">Hectogon (100)</a></li> <li><a href="/w/index.php?title=120-gon&action=edit&redlink=1" class="new" title="120-gon — pagină inexistentă">120-gon</a></li> <li><a href="/w/index.php?title=257-gon&action=edit&redlink=1" class="new" title="257-gon — pagină inexistentă">257-gon</a></li> <li><a href="/wiki/360-gon" title="360-gon">360-gon</a></li> <li><a href="/w/index.php?title=Chiliagon&action=edit&redlink=1" class="new" title="Chiliagon — pagină inexistentă">Chiliagon (1000)</a></li> <li><a href="/wiki/Miriagon" title="Miriagon">Miriagon (10 000)</a></li> <li><a href="/w/index.php?title=65537-gon&action=edit&redlink=1" class="new" title="65537-gon — pagină inexistentă">65537-gon</a></li> <li><a href="/wiki/Megagon" title="Megagon">Megagon (1 000 000)</a></li> <li><a href="/wiki/Apeirogon" title="Apeirogon">Apeirogon (∞)</a> <ul><li><a href="/wiki/Apeirogon_necoliniar" title="Apeirogon necoliniar">necoliniar</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Poligon_stelat" title="Poligon stelat">Poligoane stelate</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Pentagram%C4%83" title="Pentagramă">Pentagramă</a></li> <li><a href="/wiki/Hexagram%C4%83" title="Hexagramă">Hexagramă</a></li> <li><a href="/wiki/Heptagram%C4%83" title="Heptagramă">Heptagramă</a></li> <li><a href="/wiki/Octagram%C4%83" title="Octagramă">Octagramă</a></li> <li><a href="/wiki/Eneagram%C4%83" title="Eneagramă">Eneagramă</a></li> <li><a href="/wiki/Decagram%C4%83" title="Decagramă">Decagramă</a></li> <li><a href="/wiki/Endecagram%C4%83" title="Endecagramă">Endecagramă</a></li> <li><a href="/wiki/Dodecagram%C4%83" title="Dodecagramă">Dodecagramă</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Clase</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Poligon_bicentric" title="Poligon bicentric">Bicentrice</a></li> <li><a href="/wiki/Poligon_circumscriptibil" title="Poligon circumscriptibil">Circumscriptibile</a></li> <li><a href="/wiki/Poligon_concav" title="Poligon concav">Concave</a></li> <li><a href="/wiki/Poligon_convex" title="Poligon convex">Convexe</a></li> <li><a href="/wiki/Poligon_dual" title="Poligon dual">Duale</a></li> <li><a href="/wiki/Poligon_echilateral" title="Poligon echilateral">Echilaterale</a></li> <li><a href="/w/index.php?title=Poligon_echiunghiular&action=edit&redlink=1" class="new" title="Poligon echiunghiular — pagină inexistentă">Echiunghiulare</a></li> <li><a href="/wiki/Figur%C4%83_izogonal%C4%83" title="Figură izogonală">Izogonale</a></li> <li><a href="/wiki/Figur%C4%83_izotoxal%C4%83" title="Figură izotoxală">Izotoxale</a></li> <li><a href="/wiki/Poligon_inscriptibil" class="mw-redirect" title="Poligon inscriptibil">Inscriptibile</a></li> <li><a href="/wiki/Poligon_monoton" title="Poligon monoton">Monotone</a></li> <li><a href="/w/index.php?title=Pseudotriunghi&action=edit&redlink=1" class="new" title="Pseudotriunghi — pagină inexistentă">Pseudotriunghiuri</a></li> <li><a href="/wiki/Poligon_regulat" title="Poligon regulat">Regulate</a></li> <li><a href="/w/index.php?title=Poligon_Reinhardt&action=edit&redlink=1" class="new" title="Poligon Reinhardt — pagină inexistentă">Reinhardt</a></li> <li><a href="/wiki/Poligon_simplu" title="Poligon simplu">Simple</a></li> <li><a href="/wiki/Poligon_%C3%AEn_form%C4%83_de_stea" title="Poligon în formă de stea">Stea</a></li> <li><a href="/wiki/Poligon_str%C3%A2mb" title="Poligon strâmb">Strâmbe</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Adus de la <a dir="ltr" href="https://ro.wikipedia.org/w/index.php?title=Triunghi&oldid=14665660">https://ro.wikipedia.org/w/index.php?title=Triunghi&oldid=14665660</a></div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:Categorii" title="Special:Categorii">Categorie</a>: <ul><li><a href="/wiki/Categorie:Triunghiuri" 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Triunghi - Wikipedia