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class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_es.wikipedia.org&uselang=es" class=""><span>Donaciones</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Especial:Crear_una_cuenta&returnto=Trapezoide" title="Te recomendamos crear una cuenta e iniciar sesión; sin embargo, no es obligatorio" class=""><span>Crear una cuenta</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Especial:Entrar&returnto=Trapezoide" title="Te recomendamos iniciar sesión, aunque no es 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class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Sitio"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contenidos" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contenidos</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mover a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ocultar</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Inicio</div> </a> </li> <li id="toc-En_la_antigüedad" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#En_la_antigüedad"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>En la antigüedad</span> </div> </a> <ul id="toc-En_la_antigüedad-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tipos_de_trapezoide" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tipos_de_trapezoide"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Tipos de trapezoide</span> </div> </a> <ul id="toc-Tipos_de_trapezoide-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Características" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Características"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Características</span> </div> </a> <button aria-controls="toc-Características-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Alternar subsección Características</span> </button> <ul id="toc-Características-sublist" class="vector-toc-list"> <li id="toc-Trapezoide_cruzado" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Trapezoide_cruzado"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Trapezoide cruzado</span> </div> </a> <ul id="toc-Trapezoide_cruzado-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Trapezoide_cóncavo" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Trapezoide_cóncavo"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Trapezoide cóncavo</span> </div> </a> <ul id="toc-Trapezoide_cóncavo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Trapezoide_convexo" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Trapezoide_convexo"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Trapezoide convexo</span> </div> </a> <ul id="toc-Trapezoide_convexo-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Propiedades" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Propiedades"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Propiedades</span> </div> </a> <ul id="toc-Propiedades-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Áreas" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Áreas"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Áreas</span> </div> </a> <ul id="toc-Áreas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Véase_también" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Véase_también"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Véase también</span> </div> </a> <ul id="toc-Véase_también-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referencias" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referencias"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Referencias</span> </div> </a> <ul id="toc-Referencias-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Enlaces_externos" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Enlaces_externos"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Enlaces externos</span> </div> </a> <ul id="toc-Enlaces_externos-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="Contenidos" 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="Cambiar a la tabla de contenidos" > <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">Cambiar a la tabla de contenidos</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">Trapezoide</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="Ir a un artículo en otro idioma. Disponible en 7 idiomas" > <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-7" 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">7 idiomas</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Trapezoide" title="Trapezoide (asturiano)" lang="ast" hreflang="ast" data-title="Trapezoide" data-language-autonym="Asturianu" data-language-local-name="asturiano" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Trapezoide" title="Trapezoide (catalán)" lang="ca" hreflang="ca" data-title="Trapezoide" data-language-autonym="Català" data-language-local-name="catalán" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Trapezium" title="Trapezium (inglés)" lang="en" hreflang="en" data-title="Trapezium" data-language-autonym="English" data-language-local-name="inglés" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Trapezoido" title="Trapezoido (esperanto)" lang="eo" hreflang="eo" data-title="Trapezoido" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Trapetsoid" title="Trapetsoid (estonio)" lang="et" hreflang="et" data-title="Trapetsoid" data-language-autonym="Eesti" data-language-local-name="estonio" 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/Trapezoide" title="Trapezoide (euskera)" lang="eu" hreflang="eu" data-title="Trapezoide" data-language-autonym="Euskara" data-language-local-name="euskera" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Trapezoide" title="Trapezoide (interlingua)" lang="ia" hreflang="ia" data-title="Trapezoide" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</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/Q963655#sitelinks-wikipedia" title="Editar enlaces interlingüísticos" class="wbc-editpage">Editar enlaces</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="Espacios de nombres"> <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/Trapezoide" title="Ver la página de contenido [c]" accesskey="c"><span>Artículo</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Discusi%C3%B3n:Trapezoide" rel="discussion" title="Discusión acerca de la página [t]" accesskey="t"><span>Discusión</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Cambiar variante de idioma" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">español</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Vistas"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Trapezoide"><span>Leer</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Trapezoide&action=edit" title="Editar esta página [e]" accesskey="e"><span>Editar</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Trapezoide&action=history" title="Versiones anteriores de esta página [h]" accesskey="h"><span>Ver historial</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Página de herramientas"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Herramientas" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Herramientas</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Herramientas</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">mover a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">ocultar</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Más opciones" > <div class="vector-menu-heading"> Acciones </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Trapezoide"><span>Leer</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Trapezoide&action=edit" title="Editar esta página [e]" accesskey="e"><span>Editar</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Trapezoide&action=history"><span>Ver historial</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Especial:LoQueEnlazaAqu%C3%AD/Trapezoide" title="Lista de todas las páginas de la wiki que enlazan aquí [j]" accesskey="j"><span>Lo que enlaza aquí</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Especial:CambiosEnEnlazadas/Trapezoide" rel="nofollow" title="Cambios recientes en las páginas que enlazan con esta [k]" accesskey="k"><span>Cambios en enlazadas</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=es" title="Subir archivos [u]" accesskey="u"><span>Subir archivo</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Especial:P%C3%A1ginasEspeciales" title="Lista de todas las páginas especiales [q]" accesskey="q"><span>Páginas especiales</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Trapezoide&oldid=163046605" title="Enlace permanente a esta versión de la página"><span>Enlace permanente</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Trapezoide&action=info" title="Más información sobre esta página"><span>Información de la página</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Especial:Citar&page=Trapezoide&id=163046605&wpFormIdentifier=titleform" title="Información sobre cómo citar esta página"><span>Citar esta página</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Especial:Acortador_de_URL&url=https%3A%2F%2Fes.wikipedia.org%2Fwiki%2FTrapezoide"><span>Obtener URL acortado</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Especial:QrCode&url=https%3A%2F%2Fes.wikipedia.org%2Fwiki%2FTrapezoide"><span>Descargar código QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Imprimir/exportar </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Especial:Libro&bookcmd=book_creator&referer=Trapezoide"><span>Crear un libro</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Especial:DownloadAsPdf&page=Trapezoide&action=show-download-screen"><span>Descargar como PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Trapezoide&printable=yes" title="Versión imprimible de esta página [p]" accesskey="p"><span>Versión para imprimir</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"> En otros proyectos </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:Trapezium" hreflang="en"><span>Wikimedia 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/Q963655" title="Enlace al elemento conectado del repositorio de datos [g]" accesskey="g"><span>Elemento de Wikidata</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="Página de herramientas"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Apariencia"> <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">Apariencia</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mover a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ocultar</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">De Wikipedia, la enciclopedia libre</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="es" dir="ltr"><div class="rellink noprint hatnote"> Para otros usos de este término, véase <a href="/wiki/Trapezoide_(hueso)" class="mw-redirect" title="Trapezoide (hueso)">Trapezoide (hueso)</a>.</div> <figure typeof="mw:File/Thumb"><a href="/wiki/Archivo:%C4%8Cetrst%C5%ABris.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/%C4%8Cetrst%C5%ABris.svg/200px-%C4%8Cetrst%C5%ABris.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/%C4%8Cetrst%C5%ABris.svg/300px-%C4%8Cetrst%C5%ABris.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/%C4%8Cetrst%C5%ABris.svg/400px-%C4%8Cetrst%C5%ABris.svg.png 2x" data-file-width="550" data-file-height="550" /></a><figcaption>Trapezoide.</figcaption></figure> <p>En <a href="/wiki/Geometr%C3%ADa" title="Geometría">geometría euclídea plana</a>, un <b>trapezoide</b> es un <a href="/wiki/Cuadril%C3%A1tero" title="Cuadrilátero">cuadrilátero </a> sin lados paralelos.<sup id="cite_ref-1" class="reference separada"><a href="#cite_note-1"><span class="corchete-llamada">[</span>1<span class="corchete-llamada">]</span></a></sup> Para los <a href="/wiki/Angloparlante" class="mw-redirect" title="Angloparlante">angloparlantes</a>, <i>trapezium</i> y <i>trapezoid</i> tienen significados opuestos, según el país.<sup id="cite_ref-2" class="reference separada"><a href="#cite_note-2"><span class="corchete-llamada">[</span>2<span class="corchete-llamada">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="En_la_antigüedad"><span id="En_la_antig.C3.BCedad"></span>En la antigüedad</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trapezoide&action=edit&section=1" title="Editar sección: En la antigüedad"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Euclides" title="Euclides">Euclides</a> llama simplemente «trapecios»<sup id="cite_ref-3" class="reference separada"><a href="#cite_note-3"><span class="corchete-llamada">[</span>3<span class="corchete-llamada">]</span></a></sup> a los cuadriláteros <i>irregulares</i>, mientras que <a href="/wiki/Proclo" title="Proclo">Proclo</a> y <a href="/wiki/Arqu%C3%ADmedes" title="Arquímedes">Arquímedes</a> distinguen entre trapezoide y <a href="/wiki/Trapecio_(geometr%C3%ADa)" title="Trapecio (geometría)">trapecio</a> (con un par de lados paralelos). </p><p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Tipos_de_trapezoide">Tipos de trapezoide</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trapezoide&action=edit&section=2" title="Editar sección: Tipos de trapezoide"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Archivo:Cross-quadrilateral.png" class="mw-file-description" title="Trapezoide cruzado."><img alt="Trapezoide cruzado." src="//upload.wikimedia.org/wikipedia/commons/1/1a/Cross-quadrilateral.png" decoding="async" width="120" height="90" class="mw-file-element" data-file-width="120" data-file-height="90" /></a></span></div> <div class="gallerytext">Trapezoide cruzado.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Archivo:Kite_definition.svg" class="mw-file-description" title="Deltoide."><img alt="Deltoide." src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Kite_definition.svg/120px-Kite_definition.svg.png" decoding="async" width="120" height="94" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Kite_definition.svg/180px-Kite_definition.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Kite_definition.svg/240px-Kite_definition.svg.png 2x" data-file-width="218" data-file-height="170" /></a></span></div> <div class="gallerytext"><a href="/wiki/Deltoide" title="Deltoide">Deltoide</a>.</div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="Características"><span id="Caracter.C3.ADsticas"></span>Características</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trapezoide&action=edit&section=3" title="Editar sección: Características"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Trapezoide_cruzado">Trapezoide cruzado</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trapezoide&action=edit&section=4" title="Editar sección: Trapezoide cruzado"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Son los cuadriláteros con dos lados que se cortan, dando lugar a dos <a href="/wiki/Tri%C3%A1ngulo" title="Triángulo">triángulos</a> cuyos interiores son disjuntos. La unión de dichos interiores es el <i>interior</i> de dicho trapezoide cruzado. El cuadrilátero cruzado determina una partición del plano en tres partes. </p><p>Tiene dos diagonales disjuntas que están en el exterior AC y BD, excepto sus extremos. La <a href="/wiki/Adici%C3%B3n_(matem%C3%A1tica)" title="Adición (matemática)">suma</a> de sus <a href="/wiki/%C3%81ngulo_interior" title="Ángulo interior">ángulos interiores</a> no alcanza 360°. Los lados <b>AD</b> y <b>BC</b> prolongados sitúan el <a href="/wiki/Paralelogramo" title="Paralelogramo">paralelogramo</a> en dos <a href="/wiki/Semiplano" title="Semiplano">semiplanos</a>.<sup id="cite_ref-4" class="reference separada"><a href="#cite_note-4"><span class="corchete-llamada">[</span>4<span class="corchete-llamada">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Trapezoide_cóncavo"><span id="Trapezoide_c.C3.B3ncavo"></span>Trapezoide cóncavo</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trapezoide&action=edit&section=5" title="Editar sección: Trapezoide cóncavo"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Si consideramos el punto C <a href="/wiki/V%C3%A9rtice_(geometr%C3%ADa)" title="Vértice (geometría)">vértice</a> del <a href="/wiki/%C3%81ngulo_entrante" class="mw-redirect" title="Ángulo entrante">ángulo entrante</a>, el segmento <b>AC</b> determina dos triángulos <b>ABC</b> y <b>ACD</b>. </p><p>Tiene dos diagonales disjuntas la <b>AC</b> en el interior, la <b>BD</b> en el exterior. Los lados BC y CD con sus prolongaciones sitúan el cuadrilátero en dos semiplanos opuestos. </p> <div class="mw-heading mw-heading3"><h3 id="Trapezoide_convexo">Trapezoide convexo</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trapezoide&action=edit&section=6" title="Editar sección: Trapezoide convexo"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Se ubicò en un solo semiplano respecto de cualquier lado y de su prolongación. Un punto está en el interior del trapezoide si se ubica entre los cortes que determina una <a href="/wiki/Recta" title="Recta">recta</a>, que contiene dicho punto, con dos lados del trapezoide. Tiene dos diagonales mutuamente <a href="/wiki/Secante_(trigonometr%C3%ADa)" title="Secante (trigonometría)">secantes</a> que están en el interior de la figura. Sus ángulos suman exactamente 360°. </p><p>Se clasifican en <b>trapezoides simétricos</b>, cuyos ángulos opuestos son iguales; y,<b> trapezoides asimétricos</b> si tal caso no ocurre. Los trapezoides simétricos se llaman también <b>antiparalelogramo</b>, <b>trapezoide biisósceles</b>, <b>deltoide</b>.<sup id="cite_ref-5" class="reference separada"><a href="#cite_note-5"><span class="corchete-llamada">[</span>5<span class="corchete-llamada">]</span></a></sup><sup id="cite_ref-6" class="reference separada"><a href="#cite_note-6"><span class="corchete-llamada">[</span>6<span class="corchete-llamada">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Propiedades">Propiedades</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trapezoide&action=edit&section=7" title="Editar sección: Propiedades"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Un trapezoide puede ser inscrito en un <a href="/wiki/C%C3%ADrculo" title="Círculo">círculo</a> si la suma de algún par de ángulos opuestos es de 180° (ver <a href="/wiki/Cuadril%C3%A1tero_c%C3%ADclico" title="Cuadrilátero cíclico">cuadrilátero cíclico</a>).</li> <li>Un trapezoide puede ser circunscrito en un círculo si la suma de sus pares de lados opuestos son iguales entre sí (ver <a href="/wiki/Cuadril%C3%A1tero_tangencial" class="mw-redirect" title="Cuadrilátero tangencial">cuadrilátero tangencial</a>).</li> <li>Un trapezoide, con la definición presentada, tiene exactamente dos <a href="/wiki/Diagonal" title="Diagonal">diagonales</a>, cuyos puntos interiores están en el interior de la figura.</li> <li>Un trapezoide simétrico tiene un eje de simetría y sus diagonales son perpendiculares.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Áreas"><span id=".C3.81reas"></span>Áreas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trapezoide&action=edit&section=8" title="Editar sección: Áreas"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>En caso de los trapezoides simples (convexo y cóncavo) se descomponen en dos triángulos, se calcula las respectivas <a href="/wiki/%C3%81rea" title="Área">áreas</a> y su suma da el área buscada.</li> <li>En el caso del trapezoide cruzado, de hecho, ya hay dos triángulos de modo natural, que permiten calcular el área del trapezoide.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Véase_también"><span id="V.C3.A9ase_tambi.C3.A9n"></span>Véase también</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trapezoide&action=edit&section=9" title="Editar sección: Véase también"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Trapecio_(geometr%C3%ADa)" title="Trapecio (geometría)">Trapecio</a></li> <li><a href="/wiki/Deltoide" title="Deltoide">Deltoide</a></li> <li><a href="/wiki/Pol%C3%ADgono" title="Polígono">Polígono</a></li> <li><a href="/wiki/Rombo" title="Rombo">Rombo</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Referencias">Referencias</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trapezoide&action=edit&section=10" title="Editar sección: Referencias"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="listaref" style="list-style-type: decimal;"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><span id="CITAREFReal_Academia_Española" class="citation enciclopedia">Real Academia Española. <a rel="nofollow" class="external text" href="https://dle.rae.es/trapezoide">«trapezoide»</a>. <i>Diccionario de la lengua española</i> (23.ª edición).</span><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fes.wikipedia.org%3ATrapezoide&rft.atitle=Diccionario+de+la+lengua+espa%C3%B1ola&rft.au=Real+Academia+Espa%C3%B1ola&rft.aulast=Real+Academia+Espa%C3%B1ola&rft.btitle=trapezoide&rft.edition=23.%C2%AA&rft.genre=bookitem&rft_id=https%3A%2F%2Fdle.rae.es%2Ftrapezoide&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><span id="Reference-Mathworld-Trapezoide" class="citation web"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W</a>. <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Trapezium.html">«Trapezoide»</a>. En Weisstein, Eric W, ed. <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i> <span style="color:var(--color-subtle, #555 );">(en inglés)</span>. <a href="/wiki/Wolfram_Research" title="Wolfram Research">Wolfram Research</a>.</span><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fes.wikipedia.org%3ATrapezoide&rft.atitle=Trapezoide&rft.au=Weisstein%2C+Eric+W&rft.aulast=Weisstein%2C+Eric+W&rft.genre=article&rft.jtitle=MathWorld&rft.pub=Wolfram+Research&rft_id=http%3A%2F%2Fmathworld.wolfram.com%2FTrapezium.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Libro I, <a rel="nofollow" class="external text" href="http://www.euclides.org/menu/elements_esp/01/definicioneslibro1.htm#Definición">Proposición 22</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090306065647/http://www.euclides.org/menu/elements_esp/01/definicioneslibro1.htm#Definición">Archivado</a> el 6 de marzo de 2009 en <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. de <i>Los Elementos</i> de Euclides.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><span class="citation web"><a rel="nofollow" class="external text" href="http://roble.pntic.mec.es/jarran2/cabriweb/cuadrilat/cuadrilateros.htm">«Trapezoide»</a>.</span><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fes.wikipedia.org%3ATrapezoide&rft.btitle=Trapezoide&rft.genre=book&rft_id=http%3A%2F%2Froble.pntic.mec.es%2Fjarran2%2Fcabriweb%2Fcuadrilat%2Fcuadrilateros.htm&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">G. M. <b>Bruño</b>. Geometría Superior. </span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text">Heddy <b>Ilasaca</b>. Formulario de Ciencias. Editorial Megabyte</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Enlaces_externos">Enlaces externos</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trapezoide&action=edit&section=11" title="Editar sección: Enlaces externos"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.disfrutalasmatematicas.com/geometria/cuadrilateros.html"><i>Cuadriláteros</i></a>, en el sitio <i>Disfruta las matemáticas</i> <a rel="nofollow" class="external autonumber" href="http://www.disfrutalasmatematicas.com/index.html">[1]</a>.</li></ul> <style data-mw-deduplicate="TemplateStyles:r161257576">.mw-parser-output .mw-authority-control{margin-top:1.5em}.mw-parser-output .mw-authority-control .navbox table{margin:0}.mw-parser-output .mw-authority-control .navbox hr:last-child{display:none}.mw-parser-output .mw-authority-control .navbox+.mw-mf-linked-projects{display:none}.mw-parser-output .mw-authority-control .mw-mf-linked-projects{display:flex;padding:0.5em;border:1px solid var(--border-color-base,#a2a9b1);background-color:var(--background-color-neutral,#eaecf0);color:var(--color-base,#202122)}.mw-parser-output .mw-authority-control .mw-mf-linked-projects ul li{margin-bottom:0}.mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#a2a9b1);background-color:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .mw-authority-control .navbox-list{border-color:#f8f9fa}.mw-parser-output .mw-authority-control .navbox th{background-color:#eeeeff}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .mw-mf-linked-projects{border:1px solid var(--border-color-base,#72777d);background-color:var(--background-color-neutral,#27292d);color:var(--color-base,#eaecf0)}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral-subtle,#202122)!important}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox-list{border-color:#202122!important}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox th{background-color:#27292d!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .mw-mf-linked-projects{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral,#27292d)!important;color:var(--color-base,#eaecf0)!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral-subtle,#202122)!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox-list{border-color:#202122!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox th{background-color:#27292d!important}}</style><div class="mw-authority-control"><div role="navigation" class="navbox" aria-label="Navbox" style="width: inherit;padding:3px"><table class="hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width: 12%; text-align:center;"><a href="/wiki/Control_de_autoridades" title="Control de autoridades">Control de autoridades</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><b>Proyectos Wikimedia</b></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikidata" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> Datos:</span> <span class="uid"><a href="https://www.wikidata.org/wiki/Q963655" class="extiw" title="wikidata:Q963655">Q963655</a></span></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Commonscat"><img alt="Commonscat" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Multimedia:</span> <span class="uid"><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Trapezium">Trapezium</a></span> / <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Special:MediaSearch?type=image&search=%22Q963655%22">Q963655</a></span></span></li></ul> <hr /> </div></td></tr></tbody></table></div><div class="mw-mf-linked-projects hlist"> <ul><li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikidata" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> Datos:</span> <span class="uid"><a href="https://www.wikidata.org/wiki/Q963655" class="extiw" title="wikidata:Q963655">Q963655</a></span></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Commonscat"><img alt="Commonscat" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Multimedia:</span> <span class="uid"><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Trapezium">Trapezium</a></span> / <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Special:MediaSearch?type=image&search=%22Q963655%22">Q963655</a></span></span></li></ul> </div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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