{"id":956,"date":"2020-06-02T09:22:51","date_gmt":"2020-06-02T07:22:51","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/lehning\/?p=956"},"modified":"2021-11-05T18:47:01","modified_gmt":"2021-11-05T17:47:01","slug":"le-theoreme-de-la-mediane","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/lehning\/2020\/06\/02\/le-theoreme-de-la-mediane\/","title":{"rendered":"Le th\u00e9or\u00e8me de la m\u00e9diane"},"content":{"rendered":"<p><span style=\"font-size: 12.0pt;font-family: 'Times New Roman',serif\">Par les id\u00e9es qu\u2019elle mobilise, la d\u00e9monstration du th\u00e9or\u00e8me de la m\u00e9diane est plus int\u00e9ressante que le r\u00e9sultat lui-m\u00eame. C\u2019est cependant naturellement que nous commencerons par l\u2019\u00e9noncer. <\/span><\/p>\n<h2>Enonc\u00e9<\/h2>\n<h2><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-957 aligncenter\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/10\/Mediane.ai_-298x300.jpg\" alt=\"\" width=\"298\" height=\"300\" srcset=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/10\/Mediane.ai_-298x300.jpg 298w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/10\/Mediane.ai_-150x150.jpg 150w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/10\/Mediane.ai_.jpg 506w\" sizes=\"auto, (max-width: 298px) 100vw, 298px\" \/><\/h2>\n<p><span style=\"font-size: 12.0pt;font-family: 'Times New Roman',serif\">On consid\u00e8re un triangle ABC, I le milieu du c\u00f4t\u00e9 BC. AI est donc une m\u00e9diane du triangle. La formule suivante permet de calculer sa longueur\u00a0:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-959 aligncenter\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/10\/Mediane2.ai_.jpg\" alt=\"\" width=\"297\" height=\"63\" \/><\/p>\n<h2>D\u00e9monstration<\/h2>\n<p><span style=\"font-size: 12.0pt;line-height: 107%;font-family: 'Times New Roman',serif\">Une id\u00e9e simple pour d\u00e9montrer ce th\u00e9or\u00e8me est d\u2019utiliser la notion de vecteur car\u00a0:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-960 aligncenter\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/10\/Mediane3.ai_.jpg\" alt=\"\" width=\"235\" height=\"32\" \/><\/p>\n<p><span style=\"font-family: 'Times New Roman',serif\">En <\/span><span style=\"font-size: 12.0pt;line-height: 107%;font-family: 'Times New Roman',serif\">utilisant<\/span><span style=\"font-family: 'Times New Roman',serif\"> la notion de produit scalaire, on obtient\u00a0:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-961 aligncenter\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/10\/Mediane4.ai_.jpg\" alt=\"\" width=\"297\" height=\"97\" \/><\/p>\n<p><span style=\"font-size: 12.0pt;line-height: 107%;font-family: 'Times New Roman',serif\">En faisant la somme et en utilisant la relation\u00a0:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-962 aligncenter\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/10\/Mediane6.ai_.jpg\" alt=\"\" width=\"180\" height=\"33\" \/><\/p>\n<p><span style=\"font-size: 12.0pt;line-height: 107%;font-family: 'Times New Roman',serif\">On obtient\u00a0:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-963 aligncenter\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/10\/Mediane7.ai_-300x40.jpg\" alt=\"\" width=\"300\" height=\"40\" srcset=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/10\/Mediane7.ai_-300x40.jpg 300w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/10\/Mediane7.ai_.jpg 512w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Comme\u00a0:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-964 aligncenter\" src=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/10\/Mediane8.ai_-300x34.jpg\" alt=\"\" width=\"300\" height=\"34\" srcset=\"https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/10\/Mediane8.ai_-300x34.jpg 300w, https:\/\/blogs.futura-sciences.com\/lehning\/wp-content\/uploads\/sites\/13\/2019\/10\/Mediane8.ai_.jpg 462w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><span style=\"font-size: 12.0pt;line-height: 107%;font-family: 'Times New Roman',serif\">On en d\u00e9duit le r\u00e9sultat.<\/span><\/p>\n<!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"<p>Par les id\u00e9es qu\u2019elle mobilise, la d\u00e9monstration du th\u00e9or\u00e8me de la m\u00e9diane est plus int\u00e9ressante que le r\u00e9sultat lui-m\u00eame. C\u2019est cependant naturellement que nous commencerons par l\u2019\u00e9noncer. Enonc\u00e9 On consid\u00e8re un triangle ABC, I le milieu du c\u00f4t\u00e9 BC. AI est donc une m\u00e9diane du triangle. La formule suivante permet de calculer sa longueur\u00a0: D\u00e9monstration &hellip; <a href=\"https:\/\/blogs.futura-sciences.com\/lehning\/2020\/06\/02\/le-theoreme-de-la-mediane\/\" class=\"more-link\">Continuer la lecture de <span class=\"screen-reader-text\">Le th\u00e9or\u00e8me de la m\u00e9diane<\/span>  <span class=\"meta-nav\">&rarr;<\/span><\/a><!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt --><\/p>\n","protected":false},"author":12,"featured_media":966,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[29],"tags":[34,139,367,368],"class_list":["post-956","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-maths-2","tag-demonstration","tag-geometrie","tag-produit-scalaire","tag-vecteurs"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Le th\u00e9or\u00e8me de la m\u00e9diane, par Herv\u00e9 Lehning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blogs.futura-sciences.com\/lehning\/2020\/06\/02\/le-theoreme-de-la-mediane\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Le th\u00e9or\u00e8me de la m\u00e9diane, par Herv\u00e9 Lehning\" \/>\n<meta property=\"og:description\" content=\"Par les id\u00e9es qu\u2019elle mobilise, la d\u00e9monstration du th\u00e9or\u00e8me de la m\u00e9diane est plus int\u00e9ressante que le r\u00e9sultat lui-m\u00eame. 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