Trapéz – Wikipédia

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<span>A(z) Területe alszakasz kinyitása/becsukása</span> </button> <ul id="toc-Területe-sublist" class="vector-toc-list"> <li id="toc-Bizonyítás" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bizonyítás"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Bizonyítás</span> </div> </a> <ul id="toc-Bizonyítás-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-A_trapéz_jelentései_a_geometrián_kívül" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#A_trapéz_jelentései_a_geometrián_kívül"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>A trapéz jelentései a geometrián kívül</span> </div> </a> <ul id="toc-A_trapéz_jelentései_a_geometrián_kívül-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Külső_hivatkozások" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Külső_hivatkozások"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Külső hivatkozások</span> </div> </a> <ul id="toc-Külső_hivatkozások-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Megjegyzések" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Megjegyzések"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Megjegyzések</span> </div> </a> <ul id="toc-Megjegyzések-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="Tartalomjegyzék" 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="Tartalomjegyzék kinyitása/becsukása" > <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">Tartalomjegyzék kinyitása/becsukása</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">Trapéz</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="Ugrás egy más nyelvű szócikkre. Elérhető 99 nyelven" > <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-99" 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">99 nyelv</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Trapezoid" title="Trapezoid – angol" lang="en" hreflang="en" data-title="Trapezoid" data-language-autonym="English" data-language-local-name="angol" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Trapesium" title="Trapesium – afrikaans" lang="af" hreflang="af" data-title="Trapesium" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B4%D8%A8%D9%87_%D9%85%D9%86%D8%AD%D8%B1%D9%81" title="شبه منحرف – arab" lang="ar" hreflang="ar" data-title="شبه منحرف" data-language-autonym="العربية" data-language-local-name="arab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Trapeciu_(xeometr%C3%ADa)" title="Trapeciu (xeometría) – asztúr" lang="ast" hreflang="ast" data-title="Trapeciu (xeometría)" data-language-autonym="Asturianu" data-language-local-name="asztúr" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Trapesiya" title="Trapesiya – azerbajdzsáni" lang="az" hreflang="az" data-title="Trapesiya" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdzsáni" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BF%D0%B5%D1%86%D0%B8%D1%8F" title="Трапеция – baskír" lang="ba" hreflang="ba" data-title="Трапеция" data-language-autonym="Башҡортса" data-language-local-name="baskír" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Trapesoyd" title="Trapesoyd – Central Bikol" lang="bcl" hreflang="bcl" data-title="Trapesoyd" 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%B0%D0%BF%D0%B5%D1%86%D1%8B%D1%8F" title="Трапецыя – belarusz" lang="be" hreflang="be" data-title="Трапецыя" data-language-autonym="Беларуская" data-language-local-name="belarusz" 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%D0%B0%D0%BF%D1%8D%D1%86%D1%8B%D1%8F" title="Трапэцыя – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Трапэцыя" 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%B0%D0%BF%D0%B5%D1%86" title="Трапец – bolgár" lang="bg" hreflang="bg" data-title="Трапец" data-language-autonym="Български" data-language-local-name="bolgár" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%9F%E0%A7%8D%E0%A6%B0%E0%A6%BE%E0%A6%AA%E0%A6%BF%E0%A6%9C%E0%A6%BF%E0%A6%AF%E0%A6%BC%E0%A6%BE%E0%A6%AE" title="ট্রাপিজিয়াম – bangla" lang="bn" hreflang="bn" data-title="ট্রাপিজিয়াম" data-language-autonym="বাংলা" data-language-local-name="bangla" 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%BE%90%E0%BD%A6%E0%BC%8B%E0%BD%91%E0%BD%96%E0%BE%B1%E0%BD%B2%E0%BD%96%E0%BD%A6%E0%BC%8B" title="སྐས་དབྱིབས་ – tibeti" lang="bo" hreflang="bo" data-title="སྐས་དབྱིབས་" data-language-autonym="བོད་ཡིག" data-language-local-name="tibeti" 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/Trapez" title="Trapez – breton" lang="br" hreflang="br" data-title="Trapez" data-language-autonym="Brezhoneg" data-language-local-name="breton" 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/Trapez" title="Trapez – bosnyák" lang="bs" hreflang="bs" data-title="Trapez" data-language-autonym="Bosanski" data-language-local-name="bosnyák" 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/Trapezi" title="Trapezi – katalán" lang="ca" hreflang="ca" data-title="Trapezi" data-language-autonym="Català" data-language-local-name="katalán" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%86%DB%8C%D9%85%DA%86%DB%95%D9%84%D8%A7%D8%AA%DB%95%D8%B1%DB%8C%D8%A8" title="نیمچەلاتەریب – közép-ázsiai kurd" lang="ckb" hreflang="ckb" data-title="نیمچەلاتەریب" data-language-autonym="کوردی" data-language-local-name="közép-ázsiai kurd" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Lichob%C4%9B%C5%BEn%C3%ADk" title="Lichoběžník – cseh" lang="cs" hreflang="cs" data-title="Lichoběžník" data-language-autonym="Čeština" data-language-local-name="cseh" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BF%D0%B5%D1%86%D0%B8" title="Трапеци – csuvas" lang="cv" hreflang="cv" data-title="Трапеци" data-language-autonym="Чӑвашла" data-language-local-name="csuvas" 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/Trapesiwm" title="Trapesiwm – walesi" lang="cy" hreflang="cy" data-title="Trapesiwm" data-language-autonym="Cymraeg" data-language-local-name="walesi" 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/Trapez_(matematik)" title="Trapez (matematik) – dán" lang="da" hreflang="da" data-title="Trapez (matematik)" data-language-autonym="Dansk" data-language-local-name="dán" 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/Trapez_(Geometrie)" title="Trapez (Geometrie) – német" lang="de" hreflang="de" data-title="Trapez (Geometrie)" data-language-autonym="Deutsch" data-language-local-name="német" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A4%CF%81%CE%B1%CF%80%CE%AD%CE%B6%CE%B9%CE%BF" title="Τραπέζιο – görög" lang="el" hreflang="el" data-title="Τραπέζιο" data-language-autonym="Ελληνικά" data-language-local-name="görög" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Trapezo" title="Trapezo – eszperantó" lang="eo" hreflang="eo" data-title="Trapezo" data-language-autonym="Esperanto" data-language-local-name="eszperantó" 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/Trapecio_(geometr%C3%ADa)" title="Trapecio (geometría) – spanyol" lang="es" hreflang="es" data-title="Trapecio (geometría)" data-language-autonym="Español" data-language-local-name="spanyol" 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/Trapets" title="Trapets – észt" lang="et" hreflang="et" data-title="Trapets" data-language-autonym="Eesti" data-language-local-name="észt" 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/Trapezio" title="Trapezio – baszk" lang="eu" hreflang="eu" data-title="Trapezio" data-language-autonym="Euskara" data-language-local-name="baszk" 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/%D8%B0%D9%88%D8%B2%D9%86%D9%82%D9%87" title="ذوزنقه – perzsa" lang="fa" hreflang="fa" data-title="ذوزنقه" data-language-autonym="فارسی" data-language-local-name="perzsa" 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/Puolisuunnikas" title="Puolisuunnikas – finn" lang="fi" hreflang="fi" data-title="Puolisuunnikas" data-language-autonym="Suomi" data-language-local-name="finn" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Trap%C3%A8ze" title="Trapèze – francia" lang="fr" hreflang="fr" data-title="Trapèze" data-language-autonym="Français" data-language-local-name="francia" 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/Trapeets" title="Trapeets – északi fríz" lang="frr" hreflang="frr" data-title="Trapeets" data-language-autonym="Nordfriisk" data-language-local-name="északi fríz" 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/Traip%C3%A9isiam" title="Traipéisiam – ír" lang="ga" hreflang="ga" data-title="Traipéisiam" data-language-autonym="Gaeilge" data-language-local-name="ír" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Trapecio" title="Trapecio – gallego" lang="gl" hreflang="gl" data-title="Trapecio" data-language-autonym="Galego" data-language-local-name="gallego" 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%B8%E0%AA%AE%E0%AA%BE%E0%AA%82%E0%AA%A4%E0%AA%B0%E0%AA%AC%E0%AA%BE%E0%AA%9C%E0%AB%81_%E0%AA%9A%E0%AA%A4%E0%AB%81%E0%AA%B7%E0%AB%8D%E0%AA%95%E0%AB%8B%E0%AA%A3" title="સમાંતરબાજુ ચતુષ્કોણ – gudzsaráti" lang="gu" hreflang="gu" data-title="સમાંતરબાજુ ચતુષ્કોણ" data-language-autonym="ગુજરાતી" data-language-local-name="gudzsaráti" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%98%D7%A8%D7%A4%D7%96" title="טרפז – héber" lang="he" hreflang="he" data-title="טרפז" data-language-autonym="עברית" data-language-local-name="héber" 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%B8%E0%A4%AE%E0%A4%B2%E0%A4%AE%E0%A5%8D%E0%A4%AC_%E0%A4%9A%E0%A4%A4%E0%A5%81%E0%A4%B0%E0%A5%8D%E0%A4%AD%E0%A5%81%E0%A4%9C" title="समलम्ब चतुर्भुज – hindi" lang="hi" hreflang="hi" data-title="समलम्ब चतुर्भुज" 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/Trapez_(geometrija)" title="Trapez (geometrija) – horvát" lang="hr" hreflang="hr" data-title="Trapez (geometrija)" data-language-autonym="Hrvatski" data-language-local-name="horvát" 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/Trapec" title="Trapec – felső-szorb" lang="hsb" hreflang="hsb" data-title="Trapec" data-language-autonym="Hornjoserbsce" data-language-local-name="felső-szorb" class="interlanguage-link-target"><span>Hornjoserbsce</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8D%D5%A5%D5%B2%D5%A1%D5%B6_(%D5%A5%D6%80%D5%AF%D6%80%D5%A1%D5%B9%D5%A1%D6%83%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6)" title="Սեղան (երկրաչափություն) – örmény" lang="hy" hreflang="hy" data-title="Սեղան (երկրաչափություն)" data-language-autonym="Հայերեն" data-language-local-name="örmény" 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/Trapezio" title="Trapezio – interlingva" lang="ia" hreflang="ia" data-title="Trapezio" data-language-autonym="Interlingua" data-language-local-name="interlingva" 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/Trapesium_(geometri)" title="Trapesium (geometri) – indonéz" lang="id" hreflang="id" data-title="Trapesium (geometri)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonéz" 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/Trapezoido" title="Trapezoido – idó" lang="io" hreflang="io" data-title="Trapezoido" data-language-autonym="Ido" data-language-local-name="idó" 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/Trapisa" title="Trapisa – izlandi" lang="is" hreflang="is" data-title="Trapisa" data-language-autonym="Íslenska" data-language-local-name="izlandi" 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/Trapezio" title="Trapezio – olasz" lang="it" hreflang="it" data-title="Trapezio" data-language-autonym="Italiano" data-language-local-name="olasz" 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/%E5%8F%B0%E5%BD%A2" title="台形 – japán" lang="ja" hreflang="ja" data-title="台形" data-language-autonym="日本語" data-language-local-name="japán" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Ngapan-apan" title="Ngapan-apan – jávai" lang="jv" hreflang="jv" data-title="Ngapan-apan" data-language-autonym="Jawa" data-language-local-name="jávai" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A2%E1%83%A0%E1%83%90%E1%83%9E%E1%83%94%E1%83%AA%E1%83%98%E1%83%90" title="ტრაპეცია – grúz" lang="ka" hreflang="ka" data-title="ტრაპეცია" data-language-autonym="ქართული" data-language-local-name="grúz" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BF%D0%B5%D1%86%D0%B8%D1%8F" title="Трапеция – kazah" lang="kk" hreflang="kk" data-title="Трапеция" data-language-autonym="Қазақша" data-language-local-name="kazah" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%85%E1%9E%8F%E1%9E%BB%E1%9E%80%E1%9F%84%E1%9E%8E%E1%9E%96%E1%9F%92%E1%9E%93%E1%9E%B6%E1%9E%99" title="ចតុកោណព្នាយ – khmer" lang="km" hreflang="km" data-title="ចតុកោណព្នាយ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="khmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%82%AC%EB%8B%A4%EB%A6%AC%EA%BC%B4" title="사다리꼴 – koreai" lang="ko" hreflang="ko" data-title="사다리꼴" data-language-autonym="한국어" data-language-local-name="koreai" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BF%D0%B5%D1%86%D0%B8%D1%8F" title="Трапеция – kirgiz" lang="ky" hreflang="ky" data-title="Трапеция" data-language-autonym="Кыргызча" data-language-local-name="kirgiz" 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/Trapezium" title="Trapezium – latin" lang="la" hreflang="la" data-title="Trapezium" data-language-autonym="Latina" data-language-local-name="latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Trap%C3%A9se_(geometr%C3%ACa)" title="Trapése (geometrìa) – lombard" lang="lmo" hreflang="lmo" data-title="Trapése (geometrìa)" data-language-autonym="Lombard" data-language-local-name="lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Trapecija" title="Trapecija – litván" lang="lt" hreflang="lt" data-title="Trapecija" data-language-autonym="Lietuvių" data-language-local-name="litván" 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/Trapece" title="Trapece – lett" lang="lv" hreflang="lv" data-title="Trapece" data-language-autonym="Latviešu" data-language-local-name="lett" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BF%D0%B5%D1%86%D0%B8%D0%B9" title="Трапеций – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Трапеций" 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-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BF%D0%B5%D0%B7" title="Трапез – macedón" lang="mk" hreflang="mk" data-title="Трапез" data-language-autonym="Македонски" data-language-local-name="macedón" 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%B2%E0%B4%82%E0%B4%AC%E0%B4%95%E0%B4%82" title="ലംബകം – malajálam" lang="ml" hreflang="ml" data-title="ലംബകം" data-language-autonym="മലയാളം" data-language-local-name="malajálam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BF%D0%B5%D1%86" title="Трапец – mongol" lang="mn" hreflang="mn" data-title="Трапец" data-language-autonym="Монгол" data-language-local-name="mongol" 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%B8%E0%A4%AE%E0%A4%B2%E0%A4%82%E0%A4%AC_%E0%A4%9A%E0%A5%8C%E0%A4%95%E0%A5%8B%E0%A4%A8" title="समलंब चौकोन – maráthi" lang="mr" hreflang="mr" data-title="समलंब चौकोन" data-language-autonym="मराठी" data-language-local-name="maráthi" 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/Trapezium" title="Trapezium – maláj" lang="ms" hreflang="ms" data-title="Trapezium" data-language-autonym="Bahasa Melayu" data-language-local-name="maláj" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Trapezium" title="Trapezium – holland" lang="nl" hreflang="nl" data-title="Trapezium" data-language-autonym="Nederlands" data-language-local-name="holland" 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/Trapes_i_geometri" title="Trapes i geometri – norvég (nynorsk)" lang="nn" hreflang="nn" data-title="Trapes i geometri" data-language-autonym="Norsk nynorsk" data-language-local-name="norvég (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/Trapes_(geometri)" title="Trapes (geometri) – norvég (bokmål)" lang="nb" hreflang="nb" data-title="Trapes (geometri)" data-language-autonym="Norsk bokmål" data-language-local-name="norvég (bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%9F%E0%AD%8D%E0%AC%B0%E0%AC%BE%E0%AC%AA%E0%AC%BF%E0%AC%9C%E0%AC%BF%E0%AC%85%E0%AC%AE" title="ଟ୍ରାପିଜିଅମ – odia" lang="or" hreflang="or" data-title="ଟ୍ରାପିଜିଅମ" 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%B8%E0%A8%AE%E0%A8%B2%E0%A9%B0%E0%A8%AC_%E0%A8%9A%E0%A8%A4%E0%A9%81%E0%A8%B0%E0%A8%AD%E0%A9%81%E0%A8%9C" title="ਸਮਲੰਬ ਚਤੁਰਭੁਜ – pandzsábi" lang="pa" hreflang="pa" data-title="ਸਮਲੰਬ ਚਤੁਰਭੁਜ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pandzsábi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Trapez" title="Trapez – lengyel" lang="pl" hreflang="pl" data-title="Trapez" data-language-autonym="Polski" data-language-local-name="lengyel" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Trapessi" title="Trapessi – Piedmontese" lang="pms" hreflang="pms" data-title="Trapessi" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Trap%C3%A9zio_(geometria)" title="Trapézio (geometria) – portugál" lang="pt" hreflang="pt" data-title="Trapézio (geometria)" data-language-autonym="Português" data-language-local-name="portugál" 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/Putuq" title="Putuq – kecsua" lang="qu" hreflang="qu" data-title="Putuq" data-language-autonym="Runa Simi" data-language-local-name="kecsua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Trapez" title="Trapez – román" lang="ro" hreflang="ro" data-title="Trapez" data-language-autonym="Română" data-language-local-name="román" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BF%D0%B5%D1%86%D0%B8%D1%8F" title="Трапеция – orosz" lang="ru" hreflang="ru" data-title="Трапеция" data-language-autonym="Русский" data-language-local-name="orosz" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-se mw-list-item"><a href="https://se.wikipedia.org/wiki/Trapesa" title="Trapesa – északi számi" lang="se" hreflang="se" data-title="Trapesa" data-language-autonym="Davvisámegiella" data-language-local-name="északi számi" 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/Trapez_(geometrija)" title="Trapez (geometrija) – szerbhorvát" lang="sh" hreflang="sh" data-title="Trapez (geometrija)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="szerbhorvát" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Trapezoid" title="Trapezoid – Simple English" lang="en-simple" hreflang="en-simple" data-title="Trapezoid" 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/Lichobe%C5%BEn%C3%ADk" title="Lichobežník – szlovák" lang="sk" hreflang="sk" data-title="Lichobežník" data-language-autonym="Slovenčina" data-language-local-name="szlovák" 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/Trapez" title="Trapez – szlovén" lang="sl" hreflang="sl" data-title="Trapez" data-language-autonym="Slovenščina" data-language-local-name="szlovén" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Gonyoina_sambambiri" title="Gonyoina sambambiri – sona" lang="sn" hreflang="sn" data-title="Gonyoina sambambiri" data-language-autonym="ChiShona" data-language-local-name="sona" 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/Koor" title="Koor – szomáli" lang="so" hreflang="so" data-title="Koor" data-language-autonym="Soomaaliga" data-language-local-name="szomáli" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BF%D0%B5%D0%B7_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0)" title="Трапез (геометрија) – szerb" lang="sr" hreflang="sr" data-title="Трапез (геометрија)" data-language-autonym="Српски / srpski" data-language-local-name="szerb" 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/Trap%C3%A9sium" title="Trapésium – szundanéz" lang="su" hreflang="su" data-title="Trapésium" data-language-autonym="Sunda" data-language-local-name="szundanéz" 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/Parallelltrapets" title="Parallelltrapets – svéd" lang="sv" hreflang="sv" data-title="Parallelltrapets" data-language-autonym="Svenska" data-language-local-name="svéd" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Trapez" title="Trapez – sziléziai" lang="szl" hreflang="szl" data-title="Trapez" data-language-autonym="Ślůnski" data-language-local-name="sziléziai" 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%9A%E0%AE%B0%E0%AE%BF%E0%AE%B5%E0%AE%95%E0%AE%AE%E0%AF%8D" title="சரிவகம் – tamil" lang="ta" hreflang="ta" data-title="சரிவகம்" data-language-autonym="தமிழ்" data-language-local-name="tamil" 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%B8%E0%B0%AE%E0%B0%B2%E0%B0%82%E0%B0%AC_%E0%B0%9A%E0%B0%A4%E0%B1%81%E0%B0%B0%E0%B1%8D%E0%B0%AD%E0%B1%81%E0%B0%9C%E0%B0%82" title="సమలంబ చతుర్భుజం – telugu" lang="te" hreflang="te" data-title="సమలంబ చతుర్భుజం" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</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%B5%E0%B9%88%E0%B9%80%E0%B8%AB%E0%B8%A5%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%A1%E0%B8%84%E0%B8%B2%E0%B8%87%E0%B8%AB%E0%B8%A1%E0%B8%B9" title="รูปสี่เหลี่ยมคางหมู – thai" lang="th" hreflang="th" data-title="รูปสี่เหลี่ยมคางหมู" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Trapesi%C3%BDa" title="Trapesiýa – türkmén" lang="tk" hreflang="tk" data-title="Trapesiýa" data-language-autonym="Türkmençe" data-language-local-name="türkmén" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Trapesoid" title="Trapesoid – tagalog" lang="tl" hreflang="tl" data-title="Trapesoid" 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/Yamuk" title="Yamuk – török" lang="tr" hreflang="tr" data-title="Yamuk" data-language-autonym="Türkçe" data-language-local-name="török" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%BF%D0%B5%D1%86%D1%96%D1%8F" title="Трапеція – ukrán" lang="uk" hreflang="uk" data-title="Трапеція" data-language-autonym="Українська" data-language-local-name="ukrán" 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/%D8%B4%DA%A9%D9%84_%D9%85%D9%86%D8%AD%D8%B1%D9%81" title="شکل منحرف – urdu" lang="ur" hreflang="ur" data-title="شکل منحرف" 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/Trapetsiya" title="Trapetsiya – üzbég" lang="uz" hreflang="uz" data-title="Trapetsiya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="üzbég" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%C3%ACnh_thang" title="Hình thang – vietnámi" lang="vi" hreflang="vi" data-title="Hình thang" data-language-autonym="Tiếng Việt" data-language-local-name="vietnámi" 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/Trapezium" title="Trapezium – West Flemish" lang="vls" hreflang="vls" data-title="Trapezium" 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/Trapesoyd" title="Trapesoyd – varaó" lang="war" hreflang="war" data-title="Trapesoyd" data-language-autonym="Winaray" data-language-local-name="varaó" 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/%E6%A2%AF%E5%BD%A2" title="梯形 – wu kínai" lang="wuu" hreflang="wuu" data-title="梯形" data-language-autonym="吴语" data-language-local-name="wu kínai" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%A2%E1%83%A0%E1%83%90%E1%83%9E%E1%83%94%E1%83%AA%E1%83%98%E1%83%90" title="ტრაპეცია – Mingrelian" lang="xmf" hreflang="xmf" data-title="ტრაპეცია" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%98%D7%A8%D7%90%D7%A4%D7%A2%D7%96" title="טראפעז – jiddis" lang="yi" hreflang="yi" data-title="טראפעז" data-language-autonym="ייִדיש" data-language-local-name="jiddis" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%A2%AF%E5%BD%A2" title="梯形 – kínai" lang="zh" hreflang="zh" data-title="梯形" data-language-autonym="中文" data-language-local-name="kínai" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%A2%AF%E5%BD%A2" title="梯形 – kantoni" lang="yue" hreflang="yue" data-title="梯形" data-language-autonym="粵語" data-language-local-name="kantoni" 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/Q46303#sitelinks-wikipedia" title="Nyelvközi hivatkozások szerkesztése" class="wbc-editpage">Hivatkozások szerkesztése</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Névterek"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Trap%C3%A9z" title="A lap megtekintése [c]" accesskey="c"><span>Szócikk</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Vita:Trap%C3%A9z" 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href="/wiki/Speci%C3%A1lis:Speci%C3%A1lis_lapok" title="Az összes speciális lap listája [q]" accesskey="q"><span>Speciális lapok</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Trap%C3%A9z&oldid=27277220" title="Állandó hivatkozás ezen lap ezen változatához"><span>Hivatkozás erre a változatra</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Trap%C3%A9z&action=info" title="További információk erről a lapról"><span>Lapinformációk</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1lis:Hivatkoz%C3%A1s&page=Trap%C3%A9z&id=27277220&wpFormIdentifier=titleform" title="Információk a lap idézésével kapcsolatban"><span>Hogyan hivatkozz erre a lapra?</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1lis:UrlShortener&url=https%3A%2F%2Fhu.wikipedia.org%2Fwiki%2FTrap%25C3%25A9z"><span>Rövidített URL készítése</span></a></li><li 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változat</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Társprojektek </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Trapezoids" hreflang="en"><span>Wikimédia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q46303" title="Kapcsolt adattárelem [g]" accesskey="g"><span>Wikidata-adatlap</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Oldal eszközök"> <div id="vector-page-tools-pinned-container" 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</div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> <div id="mw-indicator-indicator-fr-review-status" class="mw-indicator"><indicator name="fr-review-status" class="mw-fr-review-status-indicator" id="mw-fr-revision-toggle"><span class="cdx-fr-css-icon-review--status--stable"></span><b>Ellenőrzött</b></indicator></div> </div> <div id="siteSub" class="noprint">A Wikipédiából, a szabad enciklopédiából</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><div id="mw-fr-revision-messages"><div id="mw-fr-revision-details" class="mw-fr-revision-details-dialog" style="display:none;"><div tabindex="0"></div><div class="cdx-dialog cdx-dialog--horizontal-actions"><header class="cdx-dialog__header cdx-dialog__header--default"><div class="cdx-dialog__header__title-group"><h2 class="cdx-dialog__header__title">Változat állapota</h2><p class="cdx-dialog__header__subtitle">Ez a lap egy ellenőrzött változata</p></div><button class="cdx-button cdx-button--action-default cdx-button--weight-quiet
							cdx-button--size-medium cdx-button--icon-only cdx-dialog__header__close-button" aria-label="Close" onclick="document.getElementById("mw-fr-revision-details").style.display = "none";" type="submit"><span class="cdx-icon cdx-icon--medium
							cdx-fr-css-icon--close"></span></button></header><div class="cdx-dialog__body">Ez a <a href="/wiki/Wikip%C3%A9dia:Jel%C3%B6lt_lapv%C3%A1ltozatok" title="Wikipédia:Jelölt lapváltozatok">közzétett változat</a>, <a class="external text" href="https://hu.wikipedia.org/w/index.php?title=Speci%C3%A1lis:Rendszernapl%C3%B3k&type=review&page=Trap%C3%A9z">ellenőrizve</a>: <i>2024. július 9.</i><p><table id="mw-fr-revisionratings-box" class="flaggedrevs-color-1" style="margin: auto;" cellpadding="0"><tr><td class="fr-text" style="vertical-align: middle;">Pontosság</td><td class="fr-value40" style="vertical-align: middle;">ellenőrzött</td></tr></table></p></div></div><div tabindex="0"></div></div></div></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="hu" dir="ltr"><figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/F%C3%A1jl:Trapez.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Trapez.svg/418px-Trapez.svg.png" decoding="async" width="418" height="246" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Trapez.svg/627px-Trapez.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/90/Trapez.svg/836px-Trapez.svg.png 2x" data-file-width="292" data-file-height="172" /></a><figcaption></figcaption></figure> <p>A <a href="/wiki/Geometria" title="Geometria">geometriában</a> <b>trapéz</b>nak nevezik az olyan <a href="/wiki/N%C3%A9gysz%C3%B6g" title="Négyszög">négyszöget</a>, amelynek van két egymással <a href="/wiki/P%C3%A1rhuzamos" class="mw-redirect" title="Párhuzamos">párhuzamos</a> oldala. </p><p>A trapéz elnevezése más nyelvekben is ugyanez (hasonló), de megesik, hogy a trapéz elnevezés alatt – szűkített értelemben – csak olyan négyszöget értenek, amelynek pontosan egy pár párhuzamos oldala van. Ilyen meghatározás előfordulhat magyar szakirodalomban is. </p><p>Ha a másik két szemközti oldal <i>szintén</i> párhuzamos egymással, akkor a trapéz egyben <a href="/wiki/Paralelogramma" title="Paralelogramma">paralelogramma</a> is. Ha nem, akkor a másik két szemközti oldalt találkozásukig meghosszabbítva egy <a href="/wiki/H%C3%A1romsz%C3%B6g" title="Háromszög">háromszöget</a> kapunk, amely tartalmazza a trapézt. </p><p>A párhuzamos oldalakat <i>alapoknak</i>, a másik két oldalt <i>száraknak</i> nevezzük. A trapéz <a href="/wiki/Magass%C3%A1g" title="Magasság">magassága</a> alatt a két párhuzamos oldalegyenes távolságát értjük. A szárak felezőpontját összekötő szakasz a trapéz középvonala, hossza egyenlő az alapok számtani közepével. </p><p>A szakirodalom (feladatgyűjtemények stb.) külön megemlít kétfajta trapézt. Az egyik az <i>egyenlő szárú trapéz</i>, a másik a <i>derékszögű trapéz</i>. </p><p>Az <i>egyenlő szárú trapéz</i> a fenti (első) definíció értelmében olyan trapéz amelynek szárai egyenlő hosszúak. Az ilyen trapéznak az alapon fekvő szögei egyenlőek, vagy egymás kiegészítőszögei. Ha az alapon fekvő szögek egyenlőek, az ilyen trapézt szimmetrikus trapéznak, illetve húrtrapéznak nevezik, mert az alapok közös felező merőlegese egyúttal <a href="/w/index.php?title=Szimmetriatengely&action=edit&redlink=1" class="new" title="Szimmetriatengely (a lap nem létezik)">szimmetriatengely</a> is, és mert van <a href="/wiki/K%C3%B6r%C3%BCl%C3%ADrt_k%C3%B6r" class="mw-redirect" title="Körülírt kör">körülírt köre</a>. </p><p>A paralelogrammára ritkán használják az „egyenlő szárú trapéz” elnevezést. Ez általában akkor van, amikor egy szövegben az „egyenlő szárú trapéz” jelenthet húrtrapézt és paralelogrammát is. A paralelogramma (mint trapéz) szárai egyenlőek, az alapon fekvő szögek azonban eltérő nagyságúak (hacsak nem téglalap is egyben), így nem igazak rá a fenti megállapítások (tengelyes szimmetria, húrnégyszögség.) </p><p>A derékszögű trapéz, mint a neve is mondja, olyan trapéz, amelynek van derékszöge. Mivel van egy pár párhuzamos oldala, így a trapéznak páros számú derékszöge van. </p><p>Egy négyszög <a href="/wiki/Akkor_%C3%A9s_csak_akkor" class="mw-redirect" title="Akkor és csak akkor">akkor és csak akkor</a> trapéz, ha van benne két szomszédos csúcs, amelynek szögei kiegészítő szögek, azaz összegük 180°. Egy másik szükséges és elégséges feltétel, hogy az <a href="/wiki/%C3%81tl%C3%B3" title="Átló">átlók</a> ugyanolyan arányban osztják fel egymást. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Területe"><span id="Ter.C3.BClete"></span>Területe</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trap%C3%A9z&action=edit&section=1" title="Szakasz szerkesztése: Területe"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A trapéz <a href="/wiki/Ter%C3%BClet_(matematika)" title="Terület (matematika)">területe</a> a következőképpen számolható: vesszük két párhuzamos oldalának <a href="/wiki/Sz%C3%A1mtani_k%C3%B6z%C3%A9p" title="Számtani közép">számtani közepét</a> és megszorozzuk a magassággal. </p><p>Tehát, ha <i>a</i> és <i>c</i> a két párhuzamos oldal, és <i>m</i> a köztük lévő távolság (magasság), a területképlet a következő: </p><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 T={\frac {a+c}{2}}m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mo>+</mo> <mi>c</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T={\frac {a+c}{2}}m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/114cecf34c0a32bb9c4f96e30f93e1296fa5bb39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.688ex; height:5.009ex;" alt="{\displaystyle T={\frac {a+c}{2}}m}"></span> </p><p>Egy másik területképlet akkor alkalmazható, ha csak a trapéz oldalainak hosszát ismerjük. Ekkor ha az oldalak rendre <i>a</i>, <i>b</i>, <i>c</i> és <i>d</i>, valamint <i>a</i> és <i>c</i> párhuzamosak (ahol <i>a</i> a hosszabbik párhuzamos oldal), akkor: </p><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 T={\frac {a+c}{4(a-c)}}{\sqrt {(a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mo>+</mo> <mi>c</mi> </mrow> <mrow> <mn>4</mn> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>−</mo> <mi>c</mi> <mo>+</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>b</mi> <mo>−</mo> <mi>c</mi> <mo>+</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>−</mo> <mi>c</mi> <mo>−</mo> <mi>d</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>+</mo> <mi>d</mi> <mo stretchy="false">)</mo> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T={\frac {a+c}{4(a-c)}}{\sqrt {(a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6312fd0c0e4642a1215c4e89767e0ad249af0a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:76.874ex; height:5.843ex;" alt="{\displaystyle T={\frac {a+c}{4(a-c)}}{\sqrt {(a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d)}}}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Bizonyítás"><span id="Bizony.C3.ADt.C3.A1s"></span>Bizonyítás</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trap%C3%A9z&action=edit&section=2" title="Szakasz szerkesztése: Bizonyítás"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Használjuk a lenti ábra jelöléseit: </p><p><span typeof="mw:File"><a href="/wiki/F%C3%A1jl:Trap%C3%A9z1201.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Trap%C3%A9z1201.png/350px-Trap%C3%A9z1201.png" decoding="async" width="350" height="164" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Trap%C3%A9z1201.png/525px-Trap%C3%A9z1201.png 1.5x, //upload.wikimedia.org/wikipedia/commons/a/a5/Trap%C3%A9z1201.png 2x" data-file-width="605" data-file-height="283" /></a></span> </p><p>Ha a D pontból párhuzamost húzunk a <i>b</i> oldallal, akkor az így keletkezett <i>DE</i> szakasz megegyezik <i>b</i>-vel. Az így kapott háromszög három oldala <i>a-c</i>, <i>b</i> és <i>d</i>. Fejezzük ki <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span>-t a <a href="/wiki/Koszinuszt%C3%A9tel" title="Koszinusztétel">koszinusztétellel</a>: </p><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 \cos \alpha ={\frac {(a-c)^{2}+d^{2}-b^{2}}{2d(a-c)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>d</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> </mrow> <mrow> <mn>2</mn> <mi>d</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \alpha ={\frac {(a-c)^{2}+d^{2}-b^{2}}{2d(a-c)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8316c379fa518bcc0b32579825a431a9a03de47" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:26.866ex; height:6.676ex;" alt="{\displaystyle \cos \alpha ={\frac {(a-c)^{2}+d^{2}-b^{2}}{2d(a-c)}}}"></span> </p><p>Ebből fejezzük ki <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 \sin \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/071763dba322940a74766aaf79f4569c5954dcf6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.73ex; height:2.176ex;" alt="{\displaystyle \sin \alpha }"></span>-t: </p><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 \cos ^{2}\alpha ={\Bigg (}{\frac {(a-c)^{2}+d^{2}-b^{2}}{2d(a-c)}}{\Bigg )}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>d</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> </mrow> <mrow> <mn>2</mn> <mi>d</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos ^{2}\alpha ={\Bigg (}{\frac {(a-c)^{2}+d^{2}-b^{2}}{2d(a-c)}}{\Bigg )}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7c9a261cdeac4bdd7357831c42ec8437a3c716c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:32.656ex; height:8.009ex;" alt="{\displaystyle \cos ^{2}\alpha ={\Bigg (}{\frac {(a-c)^{2}+d^{2}-b^{2}}{2d(a-c)}}{\Bigg )}^{2}}"></span> </p><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 \sin ^{2}\alpha =1-\cos ^{2}\alpha =1-{\Bigg (}{\frac {(a-c)^{2}+d^{2}-b^{2}}{2d(a-c)}}{\Bigg )}^{2}={\frac {4d^{2}(a-c)^{2}-{\Big (}(a-c)^{2}+d^{2}-b^{2}{\Big )}^{2}}{4d^{2}(a-c)^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mn>1</mn> <mo>−</mo> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>d</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> </mrow> <mrow> <mn>2</mn> <mi>d</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>d</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> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>4</mn> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin ^{2}\alpha =1-\cos ^{2}\alpha =1-{\Bigg (}{\frac {(a-c)^{2}+d^{2}-b^{2}}{2d(a-c)}}{\Bigg )}^{2}={\frac {4d^{2}(a-c)^{2}-{\Big (}(a-c)^{2}+d^{2}-b^{2}{\Big )}^{2}}{4d^{2}(a-c)^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd96aa022a8cbef151247c317d3486ef5e41d943" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:89.47ex; height:9.343ex;" alt="{\displaystyle \sin ^{2}\alpha =1-\cos ^{2}\alpha =1-{\Bigg (}{\frac {(a-c)^{2}+d^{2}-b^{2}}{2d(a-c)}}{\Bigg )}^{2}={\frac {4d^{2}(a-c)^{2}-{\Big (}(a-c)^{2}+d^{2}-b^{2}{\Big )}^{2}}{4d^{2}(a-c)^{2}}}}"></span> </p><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 \sin \alpha ={\frac {\sqrt {4d^{2}(a-c)^{2}-{\Big (}(a-c)^{2}+d^{2}-b^{2}{\Big )}^{2}}}{2d(a-c)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>4</mn> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>d</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> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> <mrow> <mn>2</mn> <mi>d</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \alpha ={\frac {\sqrt {4d^{2}(a-c)^{2}-{\Big (}(a-c)^{2}+d^{2}-b^{2}{\Big )}^{2}}}{2d(a-c)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f526a8e108629af56b6bf5750acc9ba28d69a2d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:46.98ex; height:9.843ex;" alt="{\displaystyle \sin \alpha ={\frac {\sqrt {4d^{2}(a-c)^{2}-{\Big (}(a-c)^{2}+d^{2}-b^{2}{\Big )}^{2}}}{2d(a-c)}}}"></span> </p><p>Az ADE háromszögben fejezzük ki <i>m</i>-et <i>d</i> és <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 \sin \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/071763dba322940a74766aaf79f4569c5954dcf6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.73ex; height:2.176ex;" alt="{\displaystyle \sin \alpha }"></span> segítségével: </p><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 m=d\cdot \sin \alpha ={\frac {\sqrt {4d^{2}(a-c)^{2}-{\Big (}(a-c)^{2}+d^{2}-b^{2}{\Big )}^{2}}}{2(a-c)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>4</mn> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>d</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> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=d\cdot \sin \alpha ={\frac {\sqrt {4d^{2}(a-c)^{2}-{\Big (}(a-c)^{2}+d^{2}-b^{2}{\Big )}^{2}}}{2(a-c)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09013790b23cf2c4d50bc0ed9a5cc52f35ca8b1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:55.014ex; height:9.843ex;" alt="{\displaystyle m=d\cdot \sin \alpha ={\frac {\sqrt {4d^{2}(a-c)^{2}-{\Big (}(a-c)^{2}+d^{2}-b^{2}{\Big )}^{2}}}{2(a-c)}}}"></span> </p><p>A szorzattá alakításokat annak segítségével végezzük el, hogy két négyzetszám különbsége felírható a két szám összegének és különbségének szorzataként: </p><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 {\frac {\sqrt {4d^{2}(a-c)^{2}-{\Big (}(a-c)^{2}+d^{2}-b^{2}{\Big )}^{2}}}{2(a-c)}}=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>4</mn> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>d</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> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sqrt {4d^{2}(a-c)^{2}-{\Big (}(a-c)^{2}+d^{2}-b^{2}{\Big )}^{2}}}{2(a-c)}}=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe248b83c98978de09a3746fc099d167daeb860f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:41.604ex; height:9.843ex;" alt="{\displaystyle {\frac {\sqrt {4d^{2}(a-c)^{2}-{\Big (}(a-c)^{2}+d^{2}-b^{2}{\Big )}^{2}}}{2(a-c)}}=}"></span> </p><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 ={\frac {\sqrt {{\Big (}2d(a-c)-(a-c)^{2}-d^{2}+b^{2}{\Big )}{\Big (}2d(a-c)+(a-c)^{2}+d^{2}-b^{2}{\Big )}}}{2(a-c)}}=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mn>2</mn> <mi>d</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>d</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> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mn>2</mn> <mi>d</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>d</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> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </msqrt> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ={\frac {\sqrt {{\Big (}2d(a-c)-(a-c)^{2}-d^{2}+b^{2}{\Big )}{\Big (}2d(a-c)+(a-c)^{2}+d^{2}-b^{2}{\Big )}}}{2(a-c)}}=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cfb0cfde01aca8f2740fa49e6d6dc3e33c88bc1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:73.719ex; height:9.843ex;" alt="{\displaystyle ={\frac {\sqrt {{\Big (}2d(a-c)-(a-c)^{2}-d^{2}+b^{2}{\Big )}{\Big (}2d(a-c)+(a-c)^{2}+d^{2}-b^{2}{\Big )}}}{2(a-c)}}=}"></span> </p><p>(Teljes négyzetté alakítás) </p><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 ={\frac {\sqrt {{\Big (}b^{2}-(a-c-d)^{2}{\Big )}{\Big (}(a-c+d)^{2}-b^{2}{\Big )}}}{2(a-c)}}=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo>−</mo> <mi>d</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo>+</mo> <mi>d</mi> <msup> <mo stretchy="false">)</mo> <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> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </msqrt> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ={\frac {\sqrt {{\Big (}b^{2}-(a-c-d)^{2}{\Big )}{\Big (}(a-c+d)^{2}-b^{2}{\Big )}}}{2(a-c)}}=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03de07957892f39e906d55ec992b0bf11419d2dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:47.396ex; height:9.843ex;" alt="{\displaystyle ={\frac {\sqrt {{\Big (}b^{2}-(a-c-d)^{2}{\Big )}{\Big (}(a-c+d)^{2}-b^{2}{\Big )}}}{2(a-c)}}=}"></span> </p><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 ={\frac {\sqrt {(b-a+c+d)(b+a-c-d)(a-c+d-b)(a-c+d+b)}}{2(a-c)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mo stretchy="false">(</mo> <mi>b</mi> <mo>−</mo> <mi>a</mi> <mo>+</mo> <mi>c</mi> <mo>+</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo>+</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo>−</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo>+</mo> <mi>d</mi> <mo>−</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo>+</mo> <mi>d</mi> <mo>+</mo> <mi>b</mi> <mo stretchy="false">)</mo> </msqrt> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ={\frac {\sqrt {(b-a+c+d)(b+a-c-d)(a-c+d-b)(a-c+d+b)}}{2(a-c)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f51357461ec3176354e53902f63e6cc3b5c6fa67" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:64.735ex; height:7.009ex;" alt="{\displaystyle ={\frac {\sqrt {(b-a+c+d)(b+a-c-d)(a-c+d-b)(a-c+d+b)}}{2(a-c)}}}"></span> </p><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 m={\frac {\sqrt {(a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d)}}{2(a-c)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <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>+</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>b</mi> <mo>−</mo> <mi>c</mi> <mo>+</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>−</mo> <mi>c</mi> <mo>−</mo> <mi>d</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>+</mo> <mi>d</mi> <mo stretchy="false">)</mo> </msqrt> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m={\frac {\sqrt {(a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d)}}{2(a-c)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/574d153dec022f61a1fdeb4043d9163f43612d60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:69.229ex; height:7.009ex;" alt="{\displaystyle m={\frac {\sqrt {(a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d)}}{2(a-c)}}}"></span> </p><p>Ezt az <i>m</i>-et behelyettesítjük 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 T={\frac {a+c}{2}}m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mo>+</mo> <mi>c</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T={\frac {a+c}{2}}m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/114cecf34c0a32bb9c4f96e30f93e1296fa5bb39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.688ex; height:5.009ex;" alt="{\displaystyle T={\frac {a+c}{2}}m}"></span> képletbe: </p><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 T={\frac {a+c}{2}}\cdot {\frac {\sqrt {(a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d)}}{2(a-c)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mo>+</mo> <mi>c</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <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>+</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>b</mi> <mo>−</mo> <mi>c</mi> <mo>+</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>−</mo> <mi>c</mi> <mo>−</mo> <mi>d</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>+</mo> <mi>d</mi> <mo stretchy="false">)</mo> </msqrt> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T={\frac {a+c}{2}}\cdot {\frac {\sqrt {(a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d)}}{2(a-c)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d44098f32a17508d1d717a6b3cbf45a07a08a3ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:76.417ex; height:7.009ex;" alt="{\displaystyle T={\frac {a+c}{2}}\cdot {\frac {\sqrt {(a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d)}}{2(a-c)}}}"></span> </p><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 T={\frac {a+c}{4(a-c)}}{\sqrt {(a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mo>+</mo> <mi>c</mi> </mrow> <mrow> <mn>4</mn> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>−</mo> <mi>c</mi> <mo>+</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>b</mi> <mo>−</mo> <mi>c</mi> <mo>+</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>−</mo> <mi>c</mi> <mo>−</mo> <mi>d</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>+</mo> <mi>d</mi> <mo stretchy="false">)</mo> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T={\frac {a+c}{4(a-c)}}{\sqrt {(a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6312fd0c0e4642a1215c4e89767e0ad249af0a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:76.874ex; height:5.843ex;" alt="{\displaystyle T={\frac {a+c}{4(a-c)}}{\sqrt {(a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d)}}}"></span> </p><p>Ha a trapézunk <a href="/wiki/H%C3%BArtrap%C3%A9z" title="Húrtrapéz">húrtrapéz</a>, akkor területét <a href="/wiki/Brahmagupta_t%C3%A9tel" class="mw-redirect" title="Brahmagupta tétel">Brahmagupta képletével</a> is kiszámolhatjuk hiszen ekkor <a href="/wiki/H%C3%BArn%C3%A9gysz%C3%B6g" title="Húrnégyszög">húrnégyszög</a> is egyben. </p> <div class="mw-heading mw-heading2"><h2 id="A_trapéz_jelentései_a_geometrián_kívül"><span id="A_trap.C3.A9z_jelent.C3.A9sei_a_geometri.C3.A1n_k.C3.ADv.C3.BCl"></span>A trapéz jelentései a geometrián kívül</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trap%C3%A9z&action=edit&section=3" title="Szakasz szerkesztése: A trapéz jelentései a geometrián kívül"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ezek az elnevezések a geometriai kifejezésből erednek: </p> <ul><li>Az <a href="/w/index.php?title=Akrobatika&action=edit&redlink=1" class="new" title="Akrobatika (a lap nem létezik)">akrobatikában</a> formájáról <i>trapéz</i>nak nevezik a két kötélen függő vízszintes rúdból álló lengő nyújtót.</li> <li>Az <a href="/wiki/Anat%C3%B3mia" title="Anatómia">anatómiában</a> a <i><a href="/wiki/Trap%C3%A9zcsont" title="Trapézcsont">trapézcsont</a></i> a <a href="/wiki/K%C3%A9z" title="Kéz">kéz</a> egy <a href="/wiki/Csont" title="Csont">csontja</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Külső_hivatkozások"><span id="K.C3.BCls.C5.91_hivatkoz.C3.A1sok"></span>Külső hivatkozások</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trap%C3%A9z&action=edit&section=4" title="Szakasz szerkesztése: Külső hivatkozások"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Trapezoid.html">"Trapezoid"</a> on <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Megjegyzések"><span id="Megjegyz.C3.A9sek"></span>Megjegyzések</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trap%C3%A9z&action=edit&section=5" title="Szakasz szerkesztése: Megjegyzések"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="ref-1col"><div 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