{"id":177,"date":"2023-04-05T03:26:13","date_gmt":"2023-04-05T03:26:13","guid":{"rendered":"https:\/\/www.wagammaths.com\/?page_id=177"},"modified":"2023-04-05T03:33:39","modified_gmt":"2023-04-05T03:33:39","slug":"theoreme-de-thales-et-sa-reciproque","status":"publish","type":"page","link":"https:\/\/www.wagammaths.com\/index.php\/3e\/theoreme-de-thales-et-sa-reciproque\/","title":{"rendered":"Th\u00e9or\u00e8me de Thal\u00e8s et sa r\u00e9ciproque"},"content":{"rendered":"<h5 style=\"text-align: justify;\"><span style=\"color: #000000;\">Th\u00e9or\u00e8me de Thal\u00e8s\u00a0: <\/span><\/h5>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Si, deux droites parall\u00e8les coupent deux droites s\u00e9cantes alors elles d\u00e9terminent deux triangles dont les c\u00f4t\u00e9s correspondants ont des longueurs proportionnelles.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"color: #0000ff;\"><strong>Remarque 1 :<\/strong><\/span> Cela revient \u00e0 dire que les triangles form\u00e9s sont semblables.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"text-decoration: underline;\"><span style=\"color: #000000; text-decoration: underline;\">Exemple<\/span><\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-178 size-medium\" src=\"https:\/\/www.wagammaths.com\/wp-content\/uploads\/2023\/04\/Thales1-300x150.png\" alt=\"Th\u00e9or\u00e8me de Thal\u00e8s\" width=\"300\" height=\"150\" srcset=\"https:\/\/www.wagammaths.com\/wp-content\/uploads\/2023\/04\/Thales1-300x150.png 300w, https:\/\/www.wagammaths.com\/wp-content\/uploads\/2023\/04\/Thales1.png 519w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <img loading=\"lazy\" decoding=\"async\" class=\"wp-image-179 size-medium alignnone\" src=\"https:\/\/www.wagammaths.com\/wp-content\/uploads\/2023\/04\/Thales2-300x221.png\" alt=\"Th\u00e9or\u00e8me de Thal\u00e8s\" width=\"300\" height=\"221\" srcset=\"https:\/\/www.wagammaths.com\/wp-content\/uploads\/2023\/04\/Thales2-300x221.png 300w, https:\/\/www.wagammaths.com\/wp-content\/uploads\/2023\/04\/Thales2.png 447w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Dans les deux cas : (ED) est parall\u00e8le \u00e0 (BC), E appartient \u00e0 (AB) et D appartient \u00e0 (AC), d\u2019apr\u00e8s le th\u00e9or\u00e8me de Thal\u00e8s, on a : <\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">\\(\\frac{AD}{AC}=\\frac{AE}{AB}=\\frac{ED}{BC}\\)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"color: #0000ff;\">Remarque 2 :<\/span> <\/strong>Le th\u00e9or\u00e8me de Thal\u00e8s permet aussi de montrer que <b>deux droites ne sont pas parall\u00e8les (par l\u2019absurde)<\/b>\u00a0en montrant qu\u2019il n\u2019y a pas d\u2019\u00e9galit\u00e9, on parlera de\u00a0<b>cons\u00e9quence du th\u00e9or\u00e8me de Thal\u00e8s<\/b>.<\/span><\/p>\n<h5><span style=\"color: #000000;\">R\u00e9ciproque du th\u00e9or\u00e8me de Thal\u00e8s\u00a0: <\/span><\/h5>\n<p><span style=\"color: #000000;\">Si, d\u2019une part les points A,D,C et d\u2019autre part les points A,E,B sont align\u00e9s dans le m\u00eame ordre et si les deux premiers rapports de Thal\u00e8s sont \u00e9gaux (\\(\\frac{AD}{AC}=\\frac{AE}{AB}\\))<\/span><span style=\"color: #000000;\">\u00a0alors les droites (DE) et (BC) sont parall\u00e8les.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Th\u00e9or\u00e8me de Thal\u00e8s\u00a0: Si, deux droites parall\u00e8les coupent deux droites s\u00e9cantes alors elles d\u00e9terminent deux triangles dont les c\u00f4t\u00e9s correspondants ont des longueurs proportionnelles. Remarque&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":65,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-177","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/pages\/177","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=177"}],"version-history":[{"count":7,"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/pages\/177\/revisions"}],"predecessor-version":[{"id":186,"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/pages\/177\/revisions\/186"}],"up":[{"embeddable":true,"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/pages\/65"}],"wp:attachment":[{"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=177"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}