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class="vector-toc-numb">2</span> <span>In elementary geometry</span> </div> </a> <ul id="toc-In_elementary_geometry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Symbols" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Symbols"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Symbols</span> </div> </a> <ul id="toc-Symbols-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Euclid" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Euclid"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Euclid</span> </div> </a> <ul id="toc-Euclid-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Conversion_to_other_units" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Conversion_to_other_units"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Conversion to other units</span> </div> </a> <ul id="toc-Conversion_to_other_units-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rule_of_3-4-5" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Rule_of_3-4-5"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Rule of 3-4-5</span> </div> </a> <ul id="toc-Rule_of_3-4-5-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Thales'_theorem" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Thales'_theorem"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Thales' theorem</span> </div> </a> <ul id="toc-Thales'_theorem-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Generalizations" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Generalizations"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Generalizations</span> </div> </a> <ul id="toc-Generalizations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>References</span> </div> </a> <ul id="toc-References-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="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <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="Toggle the table of contents" > <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">Toggle the table of contents</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">Right angle</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="Go to an article in another language. Available in 67 languages" > <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-67" 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">67 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-kbd mw-list-item"><a href="https://kbd.wikipedia.org/wiki/%D0%9F%D0%BB%D3%80%D0%B0%D0%BD%D1%8D%D0%BF%D1%8D%D0%B7%D0%B0%D0%BD%D1%89%D3%80%D1%8D" title="ПлӀанэпэзанщӀэ – Kabardian" lang="kbd" hreflang="kbd" data-title="ПлӀанэпэзанщӀэ" data-language-autonym="Адыгэбзэ" data-language-local-name="Kabardian" class="interlanguage-link-target"><span>Адыгэбзэ</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Rechter_Winkel" title="Rechter Winkel – Alemannic" lang="gsw" hreflang="gsw" data-title="Rechter Winkel" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B2%D8%A7%D9%88%D9%8A%D8%A9_%D9%82%D8%A7%D8%A6%D9%85%D8%A9" title="زاوية قائمة – Arabic" lang="ar" hreflang="ar" data-title="زاوية قائمة" data-language-autonym="العربية" data-language-local-name="Arabic" 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/%C3%81ngulu_reutu" title="Ángulu reutu – Asturian" lang="ast" hreflang="ast" data-title="Ángulu reutu" data-language-autonym="Asturianu" data-language-local-name="Asturian" 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/D%C3%BCz_bucaq" title="Düz bucaq – Azerbaijani" lang="az" hreflang="az" data-title="Düz bucaq" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%AE%E0%A6%95%E0%A7%8B%E0%A6%A3" title="সমকোণ – Bangla" lang="bn" hreflang="bn" data-title="সমকোণ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D1%80%D0%B0%D0%BC%D1%8B_%D0%B2%D1%83%D0%B3%D0%B0%D0%BB" title="Прамы вугал – Belarusian" lang="be" hreflang="be" data-title="Прамы вугал" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D1%80%D0%B0%D0%B2_%D1%8A%D0%B3%D1%8A%D0%BB" title="Прав ъгъл – Bulgarian" lang="bg" hreflang="bg" data-title="Прав ъгъл" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Rechta_W%C3%BCnki" title="Rechta Wünki – Bavarian" lang="bar" hreflang="bar" data-title="Rechta Wünki" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Pravi_ugao" title="Pravi ugao – Bosnian" lang="bs" hreflang="bs" data-title="Pravi ugao" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A2%D3%B3%D1%80%C4%95_%D0%BA%C4%95%D1%82%D0%B5%D1%81" title="Тӳрĕ кĕтес – Chuvash" lang="cv" hreflang="cv" data-title="Тӳрĕ кĕтес" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Prav%C3%BD_%C3%BAhel" title="Pravý úhel – Czech" lang="cs" hreflang="cs" data-title="Pravý úhel" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Rurama_(pimanyika)" title="Rurama (pimanyika) – Shona" lang="sn" hreflang="sn" data-title="Rurama (pimanyika)" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Angulu_rettu" title="Angulu rettu – Corsican" lang="co" hreflang="co" data-title="Angulu rettu" data-language-autonym="Corsu" data-language-local-name="Corsican" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Ongl_sgw%C3%A2r" title="Ongl sgwâr – Welsh" lang="cy" hreflang="cy" data-title="Ongl sgwâr" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Rechter_Winkel" title="Rechter Winkel – German" lang="de" hreflang="de" data-title="Rechter Winkel" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/T%C3%A4isnurk" title="Täisnurk – Estonian" lang="et" hreflang="et" data-title="Täisnurk" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9F%CF%81%CE%B8%CE%AE_%CE%B3%CF%89%CE%BD%CE%AF%CE%B1" title="Ορθή γωνία – Greek" lang="el" hreflang="el" data-title="Ορθή γωνία" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/%C3%80ngol_dr%C3%ACt_(giometr%C3%ACa)" title="Àngol drìt (giometrìa) – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Àngol drìt (giometrìa)" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C3%81ngulo_recto" title="Ángulo recto – Spanish" lang="es" hreflang="es" data-title="Ángulo recto" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Orto" title="Orto – Esperanto" lang="eo" hreflang="eo" data-title="Orto" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Angelu_zuzen" title="Angelu zuzen – Basque" lang="eu" hreflang="eu" data-title="Angelu zuzen" data-language-autonym="Euskara" data-language-local-name="Basque" 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%B2%D8%A7%D9%88%DB%8C%D9%87_%D9%82%D8%A7%D8%A6%D9%85%D9%87" title="زاویه قائمه – Persian" lang="fa" hreflang="fa" data-title="زاویه قائمه" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Angle_droit" title="Angle droit – French" lang="fr" hreflang="fr" data-title="Angle droit" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/%C3%81ngulo_recto" title="Ángulo recto – Galician" lang="gl" hreflang="gl" data-title="Ángulo recto" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A7%81%EA%B0%81" title="직각 – Korean" lang="ko" hreflang="ko" data-title="직각" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%88%D6%82%D5%B2%D5%AB%D5%B2_%D5%A1%D5%B6%D5%AF%D5%B5%D5%B8%D6%82%D5%B6" title="Ուղիղ անկյուն – Armenian" lang="hy" hreflang="hy" data-title="Ուղիղ անկյուն" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</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%95%E0%A5%8B%E0%A4%A3" title="समकोण – Hindi" lang="hi" hreflang="hi" data-title="समकोण" 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/Pravi_kut" title="Pravi kut – Croatian" lang="hr" hreflang="hr" data-title="Pravi kut" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Sudut_siku-siku" title="Sudut siku-siku – Indonesian" lang="id" hreflang="id" data-title="Sudut siku-siku" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/R%C3%A9tt_horn" title="Rétt horn – Icelandic" lang="is" hreflang="is" data-title="Rétt horn" data-language-autonym="Íslenska" data-language-local-name="Icelandic" 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/Angolo_retto" title="Angolo retto – Italian" lang="it" hreflang="it" data-title="Angolo retto" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he badge-Q70894304 mw-list-item" title=""><a href="https://he.wikipedia.org/wiki/%D7%96%D7%95%D7%95%D7%99%D7%AA_%D7%99%D7%A9%D7%A8%D7%94" title="זווית ישרה – Hebrew" lang="he" hreflang="he" data-title="זווית ישרה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Pembemraba" title="Pembemraba – Swahili" lang="sw" hreflang="sw" data-title="Pembemraba" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%A1%E0%BA%B8%E0%BA%A1%E0%BA%AA%E0%BA%B2%E0%BA%81" title="ມຸມສາກ – Lao" lang="lo" hreflang="lo" data-title="ມຸມສາກ" data-language-autonym="ລາວ" data-language-local-name="Lao" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B0%D0%B2_%D0%B0%D0%B3%D0%BE%D0%BB" title="Прав агол – Macedonian" lang="mk" hreflang="mk" data-title="Прав агол" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Zoro_mahitsy" title="Zoro mahitsy – Malagasy" lang="mg" hreflang="mg" data-title="Zoro mahitsy" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%95%E0%A4%BE%E0%A4%9F%E0%A4%95%E0%A5%8B%E0%A4%A8" title="काटकोन – Marathi" lang="mr" hreflang="mr" data-title="काटकोन" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-mzn mw-list-item"><a href="https://mzn.wikipedia.org/wiki/%D8%AF%DB%8C%DA%A9_%D8%B3%D9%88%DA%A9" title="دیک سوک – Mazanderani" lang="mzn" hreflang="mzn" data-title="دیک سوک" data-language-autonym="مازِرونی" data-language-local-name="Mazanderani" class="interlanguage-link-target"><span>مازِرونی</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Sudut_tegak" title="Sudut tegak – Malay" lang="ms" hreflang="ms" data-title="Sudut tegak" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" 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/Rechte_hoek" title="Rechte hoek – Dutch" lang="nl" hreflang="nl" data-title="Rechte hoek" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%9B%B4%E8%A7%92" title="直角 – Japanese" lang="ja" hreflang="ja" data-title="直角" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Rett_vinkel" title="Rett vinkel – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Rett vinkel" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%92%D0%B8%D1%8F%D1%88_%D0%BB%D1%83%D0%BA" title="Вияш лук – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Вияш лук" 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-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/To%CA%BBg%CA%BBri_burchak" title="Toʻgʻri burchak – Uzbek" lang="uz" hreflang="uz" data-title="Toʻgʻri burchak" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%98%E1%9E%BB%E1%9F%86%E1%9E%80%E1%9F%82%E1%9E%84" title="មុំកែង – Khmer" lang="km" hreflang="km" data-title="មុំកែង" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Khmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/K%C4%85t_prosty" title="Kąt prosty – Polish" lang="pl" hreflang="pl" data-title="Kąt prosty" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%82ngulo_reto" title="Ângulo reto – Portuguese" lang="pt" hreflang="pt" data-title="Ângulo reto" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Unghi_drept" title="Unghi drept – Romanian" lang="ro" hreflang="ro" data-title="Unghi drept" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Chiqan_chhuka" title="Chiqan chhuka – Quechua" lang="qu" hreflang="qu" data-title="Chiqan chhuka" 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%9F%D1%80%D1%8F%D0%BC%D0%BE%D0%B9_%D1%83%D0%B3%D0%BE%D0%BB" title="Прямой угол – Russian" lang="ru" hreflang="ru" data-title="Прямой угол" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/K%C3%ABndi_i_drejt%C3%AB" title="Këndi i drejtë – Albanian" lang="sq" hreflang="sq" data-title="Këndi i drejtë" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%83%E0%B7%98%E0%B6%A2%E0%B7%94_%E0%B6%9A%E0%B7%9D%E0%B6%AB" title="සෘජු කෝණ – Sinhala" lang="si" hreflang="si" data-title="සෘජු කෝණ" data-language-autonym="සිංහල" data-language-local-name="Sinhala" 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/Right_angle" 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</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="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </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> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">90° angle (π/2 radians)</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/Right_angle_(disambiguation)" class="mw-disambig" title="Right angle (disambiguation)">Right angle (disambiguation)</a>.</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Right_angle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Right_angle.svg/134px-Right_angle.svg.png" decoding="async" width="134" height="134" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Right_angle.svg/201px-Right_angle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Right_angle.svg/268px-Right_angle.svg.png 2x" data-file-width="800" data-file-height="800" /></a><figcaption>A right angle is equal to 90 degrees.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Perpendicular-coloured.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/Perpendicular-coloured.svg/220px-Perpendicular-coloured.svg.png" decoding="async" width="220" height="152" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/Perpendicular-coloured.svg/330px-Perpendicular-coloured.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/84/Perpendicular-coloured.svg/440px-Perpendicular-coloured.svg.png 2x" data-file-width="723" data-file-height="501" /></a><figcaption>A line segment (AB) drawn so that it forms right angles with a line (CD)</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd 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0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar nomobile nowraplinks" style="width:12em"><tbody><tr><th class="sidebar-title"><a href="/wiki/Angle#Types_of_angles" title="Angle">Types of angles</a></th></tr><tr><th class="sidebar-heading" style="background:#9cf"> 2D angles</th></tr><tr><td class="sidebar-content"> <p><a class="mw-selflink selflink">Right</a><br /> <a href="/wiki/Internal_and_external_angles" title="Internal and external angles">Interior</a><br /> <a href="/wiki/Internal_and_external_angles" title="Internal and external angles">Exterior</a><br /> </p> <a href="/wiki/Spherical_angle" class="mw-redirect" title="Spherical angle">Spherical</a></td> </tr><tr><th class="sidebar-heading" style="background:#9cf"> 2D angle pairs</th></tr><tr><td class="sidebar-content"> <p><a href="/wiki/Adjacent_angles" class="mw-redirect" title="Adjacent angles">Adjacent</a><br /> <a href="/wiki/Vertical_angles" class="mw-redirect" title="Vertical angles">Vertical</a><br /> <a href="/wiki/Complementary_angles" class="mw-redirect" title="Complementary angles">Complementary</a><br /> <a href="/wiki/Supplementary_angles" class="mw-redirect" title="Supplementary angles">Supplementary</a><br /> </p> <a href="/wiki/Transversal_(geometry)" title="Transversal (geometry)">Transversal</a></td> </tr><tr><th class="sidebar-heading" style="background:#9cf"> 3D angles</th></tr><tr><td class="sidebar-content"> <p><a href="/wiki/Dihedral_angle" title="Dihedral angle">Dihedral</a><br /> </p> <a href="/wiki/Solid_angle" title="Solid angle">Solid</a></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Angles" title="Template:Angles"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Angles" title="Template talk:Angles"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Angles" title="Special:EditPage/Template:Angles"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>In <a href="/wiki/Geometry" title="Geometry">geometry</a> and <a href="/wiki/Trigonometry" title="Trigonometry">trigonometry</a>, a <b>right angle</b> is an <a href="/wiki/Angle" title="Angle">angle</a> of exactly 90 <a href="/wiki/Degree_(angle)" title="Degree (angle)">degrees</a> or <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num"><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 \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span></span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> <a href="/wiki/Radian" title="Radian">radians</a><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> corresponding to a quarter <a href="/wiki/Turn_(geometry)" class="mw-redirect" title="Turn (geometry)">turn</a>.<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> If a <a href="/wiki/Line_(mathematics)#Ray" class="mw-redirect" title="Line (mathematics)">ray</a> is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles.<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> The term is a <a href="/wiki/Calque" title="Calque">calque</a> of <a href="/wiki/Latin" title="Latin">Latin</a> <i>angulus rectus</i>; here <i>rectus</i> means "upright", referring to the vertical perpendicular to a horizontal base line. </p><p>Closely related and important geometrical concepts are <a href="/wiki/Perpendicular" title="Perpendicular">perpendicular</a> lines, meaning lines that form right angles at their point of intersection, and <a href="/wiki/Orthogonality" title="Orthogonality">orthogonality</a>, which is the property of forming right angles, usually applied to <a href="/wiki/Euclidean_vector" title="Euclidean vector">vectors</a>. The presence of a right angle in a <a href="/wiki/Triangle" title="Triangle">triangle</a> is the defining factor for <a href="/wiki/Right_triangle" title="Right triangle">right triangles</a>,<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> making the right angle basic to trigonometry. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Etymology">Etymology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Right_angle&action=edit&section=1" title="Edit section: Etymology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The meaning of <i>right</i> in <i>right angle</i> possibly refers to the <a href="/wiki/Classical_Latin" title="Classical Latin">Latin</a> adjective <i>rectus</i> 'erect, straight, upright, perpendicular'. A <a href="/wiki/Greek_language" title="Greek language">Greek</a> equivalent is <i>orthos</i> 'straight; perpendicular' (see <a href="/wiki/Orthogonality" title="Orthogonality">orthogonality</a>). </p> <div class="mw-heading mw-heading2"><h2 id="In_elementary_geometry">In elementary geometry</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Right_angle&action=edit&section=2" title="Edit section: In elementary geometry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <a href="/wiki/Rectangle" title="Rectangle">rectangle</a> is a <a href="/wiki/Quadrilateral" title="Quadrilateral">quadrilateral</a> with four right angles. A <a href="/wiki/Square" title="Square">square</a> has four right angles, in addition to equal-length sides. </p><p>The <a href="/wiki/Pythagorean_theorem" title="Pythagorean theorem">Pythagorean theorem</a> states how to determine when a triangle is a <a href="/wiki/Right_triangle" title="Right triangle">right triangle</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Symbols">Symbols</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Right_angle&action=edit&section=3" title="Edit section: Symbols"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Rtriangle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Rtriangle.svg/220px-Rtriangle.svg.png" decoding="async" width="220" height="189" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Rtriangle.svg/330px-Rtriangle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Rtriangle.svg/440px-Rtriangle.svg.png 2x" data-file-width="512" data-file-height="440" /></a><figcaption>Right triangle, with the right angle shown via a small square</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Triangle_30-60-90_rotated.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Triangle_30-60-90_rotated.png/220px-Triangle_30-60-90_rotated.png" decoding="async" width="220" height="181" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/1/15/Triangle_30-60-90_rotated.png 1.5x" data-file-width="256" data-file-height="211" /></a><figcaption>Another option of diagrammatically indicating a right angle, using an angle curve and a small dot</figcaption></figure> <p>In <a href="/wiki/Unicode" title="Unicode">Unicode</a>, the symbol for a right angle is <span class="nowrap"><style data-mw-deduplicate="TemplateStyles:r886049734">.mw-parser-output .monospaced{font-family:monospace,monospace}</style><span class="monospaced">U+221F</span> </span><span style="font-size:125%;line-height:1em">∟</span> <span style="font-variant: small-caps; text-transform: lowercase;">RIGHT ANGLE</span> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">&angrt;</span>). It should not be confused with the similarly shaped symbol <span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">U+231E</span> </span><span style="font-size:125%;line-height:1em">⌞</span> <span style="font-variant: small-caps; text-transform: lowercase;">BOTTOM LEFT CORNER</span> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">&dlcorn;, &llcorner;</span>). Related symbols are <span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">U+22BE</span> </span><span style="font-size:125%;line-height:1em">⊾</span> <span style="font-variant: small-caps; text-transform: lowercase;">RIGHT ANGLE WITH ARC</span> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">&angrtvb;</span>), <span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">U+299C</span> </span><span style="font-size:125%;line-height:1em">⦜</span> <span style="font-variant: small-caps; text-transform: lowercase;">RIGHT ANGLE VARIANT WITH SQUARE</span> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">&vangrt;</span>), and <span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">U+299D</span> </span><span style="font-size:125%;line-height:1em">⦝</span> <span style="font-variant: small-caps; text-transform: lowercase;">MEASURED RIGHT ANGLE WITH DOT</span> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">&angrtvbd;</span>).<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> </p><p>In diagrams, the fact that an angle is a right angle is usually expressed by adding a small right angle that forms a square with the angle in the diagram, as seen in the diagram of a right triangle (in British English, a right-angled triangle) to the right. The symbol for a measured angle, an arc, with a dot, is used in some European countries, including German-speaking countries and Poland, as an alternative symbol for a right angle.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Euclid">Euclid</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Right_angle&action=edit&section=4" title="Edit section: Euclid"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Right angles are fundamental in <a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements">Euclid's Elements</a>. They are defined in Book 1, definition 10, which also defines perpendicular lines. Definition 10 does not use numerical degree measurements but rather touches at the very heart of what a right angle is, namely two straight lines intersecting to form two equal and adjacent angles.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The straight lines which form right angles are called perpendicular.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Euclid uses right angles in definitions 11 and 12 to define acute angles (those smaller than a right angle) and obtuse angles (those greater than a right angle).<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Two angles are called <a href="/wiki/Complementary_angles" class="mw-redirect" title="Complementary angles">complementary</a> if their sum is a right angle.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>Book 1 Postulate 4 states that all right angles are equal, which allows Euclid to use a right angle as a unit to measure other angles with. Euclid's commentator <a href="/wiki/Proclus" title="Proclus">Proclus</a> gave a proof of this postulate using the previous postulates, but it may be argued that this proof makes use of some hidden assumptions. <a href="/wiki/Giovanni_Girolamo_Saccheri" title="Giovanni Girolamo Saccheri">Saccheri</a> gave a proof as well but using a more explicit assumption. In <a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</a>'s <a href="/wiki/Hilbert%27s_axioms" title="Hilbert's axioms">axiomatization of geometry</a> this statement is given as a theorem, but only after much groundwork. One may argue that, even if postulate 4 can be proven from the preceding ones, in the order that Euclid presents his material it is necessary to include it since without it postulate 5, which uses the right angle as a unit of measure, makes no sense.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Conversion_to_other_units">Conversion to other units</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Right_angle&action=edit&section=5" title="Edit section: Conversion to other units"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A right angle may be expressed in different units: </p> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">4</span></span>⁠</span> <a href="/wiki/Turn_(geometry)" class="mw-redirect" title="Turn (geometry)">turn</a></li> <li>90° (<a href="/wiki/Degree_(angle)" title="Degree (angle)">degrees</a>)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">π</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> <a href="/wiki/Radian" title="Radian">radians</a></li> <li>100 <a href="/wiki/Grad_(angle)" class="mw-redirect" title="Grad (angle)">grad</a> (also called <i>grade</i>, <i>gradian</i>, or <i>gon</i>)</li> <li>8 points (of a 32-point <a href="/wiki/Compass_rose" title="Compass rose">compass rose</a>)</li> <li>6 hours (astronomical <a href="/wiki/Hour_angle" title="Hour angle">hour angle</a>)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Rule_of_3-4-5">Rule of 3-4-5</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Right_angle&action=edit&section=6" title="Edit section: Rule of 3-4-5"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Throughout history, carpenters and masons have known a quick way to confirm if an angle is a true right angle. It is based on the <a href="/wiki/Pythagorean_triple" title="Pythagorean triple">Pythagorean triple</a> <span class="nowrap">(3, 4, 5)</span> and the rule of 3-4-5. From the angle in question, running a straight line along one side exactly three units in length, and along the second side exactly four units in length, will create a <a href="/wiki/Hypotenuse" title="Hypotenuse">hypotenuse</a> (the longer line opposite the right angle that connects the two measured endpoints) of exactly five units in length. </p> <div class="mw-heading mw-heading2"><h2 id="Thales'_theorem"><span id="Thales.27_theorem"></span>Thales' theorem</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Right_angle&action=edit&section=7" title="Edit section: Thales' theorem"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1273380762/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti 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.trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:499px;max-width:499px"><div class="trow"><div class="tsingle" style="width:256px;max-width:256px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:01-Rechter_Winkel_mittels_Thaleskreis.gif" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/01-Rechter_Winkel_mittels_Thaleskreis.gif/254px-01-Rechter_Winkel_mittels_Thaleskreis.gif" decoding="async" width="254" height="195" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/01-Rechter_Winkel_mittels_Thaleskreis.gif/381px-01-Rechter_Winkel_mittels_Thaleskreis.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/d/df/01-Rechter_Winkel_mittels_Thaleskreis.gif 2x" data-file-width="450" data-file-height="345" /></a></span></div><div class="thumbcaption">Construction of the perpendicular to the half-line h from the point P (applicable not only at the end point A, M is freely selectable), animation at the end with pause 10 s</div></div><div class="tsingle" style="width:239px;max-width:239px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:01-Rechter_Winkel_mittels_Thaleskreis-II.gif" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/01-Rechter_Winkel_mittels_Thaleskreis-II.gif/237px-01-Rechter_Winkel_mittels_Thaleskreis-II.gif" decoding="async" width="237" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/01-Rechter_Winkel_mittels_Thaleskreis-II.gif/356px-01-Rechter_Winkel_mittels_Thaleskreis-II.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/e/e8/01-Rechter_Winkel_mittels_Thaleskreis-II.gif 2x" data-file-width="390" data-file-height="336" /></a></span></div><div class="thumbcaption">Alternative construction if P outside of the half-line h and the distance A to P' is small (B is freely selectable),<br />animation at the end with pause 10 s</div></div></div></div></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Thales%27_theorem" class="mw-redirect" title="Thales' theorem">Thales' theorem</a></div> <p>Thales' theorem states that an angle inscribed in a <a href="/wiki/Semicircle" title="Semicircle">semicircle</a> (with a vertex on the semicircle and its defining rays going through the endpoints of the semicircle) is a right angle. </p><p>Two application examples in which the right angle and the Thales' theorem are included (see animations). </p> <div class="mw-heading mw-heading2"><h2 id="Generalizations">Generalizations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Right_angle&action=edit&section=8" title="Edit section: Generalizations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Solid_angle" title="Solid angle">solid angle</a> subtended by an <a href="/wiki/Octant_of_a_sphere" title="Octant of a sphere">octant of a sphere</a> (the spherical triangle with three right angles) equals <span class="texhtml mvar" style="font-style:italic;">π</span>/2  <a href="/wiki/Steradian" title="Steradian">sr</a>.<sup id="cite_ref-u421_12-0" class="reference"><a href="#cite_note-u421-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Right_angle&action=edit&section=9" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul 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system">Cartesian coordinate system</a></li> <li><a href="/wiki/Angle#Types_of_angles" title="Angle">Types of angles</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Right_angle&action=edit&section=10" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.mathopenref.com/angleright.html">"Right Angle"</a>. <i>Math Open Reference</i><span class="reference-accessdate">. Retrieved <span class="nowrap">26 April</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Math+Open+Reference&rft.atitle=Right+Angle&rft_id=http%3A%2F%2Fwww.mathopenref.com%2Fangleright.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARight+angle" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Wentworth p. 11</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">Wentworth p. 8</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Wentworth p. 40</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Unicode 5.2 Character Code Charts <a rel="nofollow" class="external text" href="https://www.unicode.org/charts/PDF/U2200.pdf">Mathematical Operators</a>, <a rel="nofollow" class="external text" href="https://www.unicode.org/charts/PDF/U2980.pdf">Miscellaneous Mathematical Symbols-B</a></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMüller-PhilippGorski2011" class="citation book cs1 cs1-prop-foreign-lang-source">Müller-Philipp, Susanne; Gorski, Hans-Joachim (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=PAdSPOBYHPUC"><i>Leitfaden Geometrie</i></a> [<i>Handbook Geometry</i>] (in German). Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783834886163" title="Special:BookSources/9783834886163"><bdi>9783834886163</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Leitfaden+Geometrie&rft.pub=Springer&rft.date=2011&rft.isbn=9783834886163&rft.aulast=M%C3%BCller-Philipp&rft.aufirst=Susanne&rft.au=Gorski%2C+Hans-Joachim&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DPAdSPOBYHPUC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARight+angle" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Heath p. 181</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">Heath p. 181</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">Heath p. 181</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">Wentworth p. 9</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Heath pp. 200–201 for the paragraph</span> </li> <li id="cite_note-u421-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-u421_12-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://planetmath.org/octant">"octant"</a>. <i>PlanetMath.org</i>. 2013-03-22<span class="reference-accessdate">. Retrieved <span class="nowrap">2024-10-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=PlanetMath.org&rft.atitle=octant&rft.date=2013-03-22&rft_id=https%3A%2F%2Fplanetmath.org%2Foctant&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARight+angle" class="Z3988"></span></span> </li> </ol></div></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWentworth1895" class="citation book cs1">Wentworth, G.A. (1895). <a rel="nofollow" class="external text" href="https://archive.org/details/atextbookgeomet05wentgoog"><i>A Text-Book of Geometry</i></a>. Ginn & Co.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Text-Book+of+Geometry&rft.pub=Ginn+%26+Co.&rft.date=1895&rft.aulast=Wentworth&rft.aufirst=G.A.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fatextbookgeomet05wentgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARight+angle" class="Z3988"></span></li> <li>Euclid, commentary and trans. by <a href="/wiki/T._L._Heath" class="mw-redirect" title="T. L. Heath">T. L. 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