{"id":7435,"date":"2022-04-01T13:50:08","date_gmt":"2022-04-01T11:50:08","guid":{"rendered":"https:\/\/www.mathweb.fr\/euclide\/?p=7435"},"modified":"2022-04-01T13:50:09","modified_gmt":"2022-04-01T11:50:09","slug":"determiner-la-mesure-dun-angle-dans-cette-configuration","status":"publish","type":"post","link":"https:\/\/www.mathweb.fr\/euclide\/2022\/04\/01\/determiner-la-mesure-dun-angle-dans-cette-configuration\/","title":{"rendered":"D\u00e9terminer la mesure d&rsquo;un angle dans cette configuration"},"content":{"rendered":"\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"478\" height=\"327\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/pb_geometrie.png\" alt=\"d\u00e9terminer angle\" class=\"wp-image-7436\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/pb_geometrie.png 478w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/pb_geometrie-300x205.png 300w\" sizes=\"auto, (max-width: 478px) 100vw, 478px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u00c9tant donn\u00e9 un triangle ABC, isoc\u00e8le en A et tel que \\( \\widehat{BAC}=100^\\circ \\), on consid\u00e8re un point D sur [AB) tel que AD = BC.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Il s&rsquo;agit ici de d\u00e9terminer la mesure de l&rsquo;angle \\( \\widehat{ADC} \\) sans consigne.<\/p>\n\n\n\n<!--more-->\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Au menu sur cette page...<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.mathweb.fr\/euclide\/2022\/04\/01\/determiner-la-mesure-dun-angle-dans-cette-configuration\/#Une_prise_dinitiative_introduire_un_autre_point\" >Une prise d&rsquo;initiative: introduire un autre point<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.mathweb.fr\/euclide\/2022\/04\/01\/determiner-la-mesure-dun-angle-dans-cette-configuration\/#Les_fichiers_sources_Geogebra\" >Les fichiers sources G\u00e9ogebra<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Une_prise_dinitiative_introduire_un_autre_point\"><\/span>Une prise d&rsquo;initiative: introduire un autre point<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Il existe sans doute plusieurs m\u00e9thodes, dont celle qui suit. Cette m\u00e9thode peut \u00eatre comprise d\u00e8s le coll\u00e8ge. Nous allons consid\u00e9rer le point E de sorte que ADE soit isoc\u00e8le en E:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"469\" height=\"308\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image.png\" alt=\"\" class=\"wp-image-7437\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image.png 469w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-300x197.png 300w\" sizes=\"auto, (max-width: 469px) 100vw, 469px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u00c9tant isoc\u00e8le en E, on peut facilement en d\u00e9duire que \\( \\widehat{EAD} = \\widehat{ADE} = 40^\\circ \\).<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"463\" height=\"306\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-1.png\" alt=\"\" class=\"wp-image-7438\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-1.png 463w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-1-300x198.png 300w\" sizes=\"auto, (max-width: 463px) 100vw, 463px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ainsi, \\( \\widehat{EAC} = 60^\\circ \\). Comme le triangle EAC est isoc\u00e8le en A, cela signifie qu&rsquo;il est \u00e9quilat\u00e9ral.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"467\" height=\"309\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-2.png\" alt=\"\" class=\"wp-image-7439\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-2.png 467w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-2-300x199.png 300w\" sizes=\"auto, (max-width: 467px) 100vw, 467px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Le triangle CED est alors isoc\u00e8le en E.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Le triangle ABC est isoc\u00e8le en A avec \\( \\widehat{BAC} = 100^\\circ \\) donc \\( \\widehat{ABC} = \\widehat{ACB} = 40^\\circ \\). Comme \\( \\widehat{ABD} \\) est un angle plat, on en d\u00e9duit que \\(\\widehat{DBC}=140^\\circ\\).<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"466\" height=\"314\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-3.png\" alt=\"\" class=\"wp-image-7440\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-3.png 466w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-3-300x202.png 300w\" sizes=\"auto, (max-width: 466px) 100vw, 466px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">On en d\u00e9duit alors que \\( \\widehat{BCE} = 20^\\circ \\) car, ne l&rsquo;oublions pas, ACE est \u00e9quilat\u00e9ral et donc \\(\\widehat{ACE}=60^\\circ\\).<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"472\" height=\"315\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-4.png\" alt=\"\" class=\"wp-image-7441\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-4.png 472w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-4-300x200.png 300w\" sizes=\"auto, (max-width: 472px) 100vw, 472px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Dans le quadrilat\u00e8re CEDB, la somme de la mesure des angles est \u00e9gale \u00e0 360\u00b0. Cela signifie donc que \\(\\widehat{CED}=360-40-140-20=160^\\circ\\).<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"467\" height=\"314\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-6.png\" alt=\"\" class=\"wp-image-7443\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-6.png 467w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-6-300x202.png 300w\" sizes=\"auto, (max-width: 467px) 100vw, 467px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Le triangle CED \u00e9tant isoc\u00e8le en E, on en d\u00e9duit que \\(\\widehat{ECD}=\\widehat{EDC}=10^\\circ\\).<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"478\" height=\"322\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-7.png\" alt=\"\" class=\"wp-image-7445\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-7.png 478w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/image-7-300x202.png 300w\" sizes=\"auto, (max-width: 478px) 100vw, 478px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ainsi, \\( \\widehat{ADC} = \\widehat{ADE} &#8211; \\widehat{EDC} = 40-10=30^\\circ. \\)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Les_fichiers_sources_Geogebra\"><\/span>Les fichiers sources G\u00e9ogebra<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<div class=\"wp-block-file aligncenter\"><a id=\"wp-block-file--media-558bb563-f849-4e1c-85ab-3b194d23b72a\" href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/mesure-angle.zip\">mesure-angle<\/a><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/04\/mesure-angle.zip\" class=\"wp-block-file__button\" download aria-describedby=\"wp-block-file--media-558bb563-f849-4e1c-85ab-3b194d23b72a\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ce probl\u00e8me a \u00e9t\u00e9 trait\u00e9 dans la vid\u00e9o suivante:<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"A good isosceles triangle problem\" width=\"750\" height=\"422\" src=\"https:\/\/www.youtube.com\/embed\/NFpsuIaHGQs?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>\u00c9tant donn\u00e9 un triangle ABC, isoc\u00e8le en A et tel que \\( \\widehat{BAC}=100^\\circ \\), on consid\u00e8re un point D sur [AB) tel que AD = BC. Il s&rsquo;agit ici de d\u00e9terminer la mesure de l&rsquo;angle \\( \\widehat{ADC} \\) sans consigne.<\/p>\n","protected":false},"author":1,"featured_media":7448,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[340,52],"class_list":["post-7435","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematiques","tag-angle","tag-geometrie"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>D\u00e9terminer la mesure d&#039;un angle dans cette configuration - Mathweb.fr<\/title>\n<meta name=\"description\" content=\"Le but de ce probl\u00e8me est de d\u00e9terminer la mesure d&#039;un angle dans une configuration bien pr\u00e9cise. 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