{"id":1610,"date":"2017-09-29T10:18:55","date_gmt":"2017-09-29T15:18:55","guid":{"rendered":"http:\/\/pascal-tic.org\/math\/?page_id=1610"},"modified":"2017-10-03T11:30:49","modified_gmt":"2017-10-03T16:30:49","slug":"enonces-de-geometrie","status":"publish","type":"page","link":"https:\/\/pascal-tic.org\/math\/enonces-de-geometrie\/","title":{"rendered":"\u00c9nonc\u00e9s de g\u00e9om\u00e9trie"},"content":{"rendered":"<section class=\"l-section wpb_row height_medium\"><div class=\"l-section-h i-cf\"><div class=\"g-cols vc_row via_flex valign_top type_default\"><div class=\"vc_col-sm-12 wpb_column vc_column_container\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\"><div class=\"wpb_text_column\"><div class=\"wpb_wrapper\"><p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\"><b>\u00c9NONC\u00c9S<\/b><\/span><\/span><\/p>\n<ol>\n<li><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Les angles oppos\u00e9s par le sommet sont isom\u00e9triques.<\/span><\/span><\/li>\n<\/ol>\n<ol start=\"2\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">La somme des mesures des angles int\u00e9rieurs d\u2019un triangle est 180\u00b0.<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"3\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Si une s\u00e9cante coupe deux droites parall\u00e8les, alors les angles [correspondants, alternes-internes ou alternes-externes] sont isom\u00e9triques.<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"4\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Si deux angles correspondants, alternes-internes ou alternes-externes sont isom\u00e9triques, alors ils sont form\u00e9s par des droites parall\u00e8les coup\u00e9es par une s\u00e9cante.<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"5\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Deux droites perpendiculaires \u00e0 une troisi\u00e8me sont parall\u00e8les entre elles.<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"6\">\n<li><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\"><span lang=\"fr-FR\"><b>Th\u00e9or\u00e8me de Pythagore<\/b><\/span><\/span><\/span><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\"><span lang=\"fr-FR\">\u00a0: dans un triangle rectangle, le carr\u00e9 de la longueur de l\u2019hypot\u00e9nuse est \u00e9gal \u00e0 la somme des carr\u00e9s des longueurs des deux autres c\u00f4t\u00e9s.<\/span><\/span><\/span><\/li>\n<\/ol>\n<ol start=\"7\">\n<li>\n<p lang=\"fr-FR\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\"><b>Propri\u00e9t\u00e9 de l\u2019angle de 30\u00b0<\/b><\/span><\/span><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">\u00a0: dans un triangle rectangle, le c\u00f4t\u00e9 oppos\u00e9 \u00e0 l\u2019angle de 30\u00b0 mesure la moiti\u00e9 de l\u2019hypot\u00e9nuse.<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"8\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\"><b>Propri\u00e9t\u00e9 de l\u2019angle de 45\u00b0\u00a0<\/b><\/span><\/span><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">: un triangle rectangle poss\u00e9dant un angle de 45\u00b0 est isoc\u00e8le.<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"9\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Dans un triangle rectangle, les angles aigus sont compl\u00e9mentaires.<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"10\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Dans un triangle isoc\u00e8le, les angles oppos\u00e9s aux c\u00f4t\u00e9s isom\u00e9triques sont isom\u00e9triques.<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"11\">\n<li>\n<p align=\"justify\"><span style=\"color: #000000;\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Des <\/span><\/span><\/span><em><span style=\"color: #000000;\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">figures \u00e9quivalentes<\/span><\/span><\/span><\/em><span style=\"color: #000000;\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\"> sont des figures de m\u00eame aire.<\/span><\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"12\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Des solides \u00e9quivalents sont des solides de m\u00eame volume.<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\"><u><b>Triangles isom\u00e9triques<\/b><\/u><\/span><\/span><\/p>\n<ol start=\"13\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Deux triangles qui ont tous leurs c\u00f4t\u00e9s homologues isom\u00e9triques sont isom\u00e9triques. (C-C-C)<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"14\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Deux triangles qui ont un angle isom\u00e9trique compris entre des c\u00f4t\u00e9s homologues isom\u00e9triques sont isom\u00e9triques. (C-A-C)<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"15\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Deux triangles qui ont un c\u00f4t\u00e9 isom\u00e9trique compris entre des angles homologues isom\u00e9triques sont isom\u00e9triques. (A-C-A)<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"16\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Dans les triangles isom\u00e9triques, tous les angles et tous les c\u00f4t\u00e9s homologues ont la m\u00eame mesure.<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\"><u><b>Triangles semblables<\/b><\/u><\/span><\/span><\/p>\n<ol start=\"17\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Deux triangles dont les mesures des c\u00f4t\u00e9s homologues sont proportionnelles sont semblables. (C-C-C)<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"18\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Deux triangles poss\u00e9dant un angle isom\u00e9trique compris entre des c\u00f4t\u00e9s homologues de longueurs proportionnelles sont semblables. (C-A-C)<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"19\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Deux triangles qui ont deux angles homologues isom\u00e9triques sont semblables. (A-A)<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"20\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Des figures semblables ont toutes les mesures de leurs segments homologues proportionnelles.<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"21\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Des figures semblables ont tous leurs angles homologues isom\u00e9triques.<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"22\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">Toute droite s\u00e9cante \u00e0 deux c\u00f4t\u00e9s d\u2019un triangle et parall\u00e8le au troisi\u00e8me c\u00f4t\u00e9 forme un petit triangle semblable au grand.<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\"><u><b>Relations m\u00e9triques<\/b><\/u><\/span><\/span><\/p>\n<ol start=\"23\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\"><b>Th\u00e9or\u00e8me de la cath\u00e8te<\/b><\/span><\/span><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">\u00a0: dans un triangle rectangle, la mesure de chaque c\u00f4t\u00e9 de l\u2019angle droit est la moyenne proportionnelle de la mesure de sa projection sur l\u2019hypot\u00e9nuse et de celle de l\u2019hypot\u00e9nuse enti\u00e8re.<\/span><\/span><\/p>\n<\/li>\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\"><b>Th\u00e9or\u00e8me de la hauteur relative \u00e0 l\u2019hypot\u00e9nuse\u00a0<\/b><\/span><\/span><span style=\"font-family: Century Gothic,serif;\"><u><b>:<\/b><\/u><\/span><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\"> Dans un triangle rectangle, la mesure de la hauteur issue du sommet de l\u2019angle droit est la moyenne proportionnelle des mesures des deux segments qu\u2019elle d\u00e9termine sur l\u2019hypot\u00e9nuse.<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<ol start=\"25\">\n<li>\n<p align=\"justify\"><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\"><b>Th\u00e9or\u00e8me du produit des cath\u00e8tes<\/b><\/span><\/span><span style=\"font-family: Century Gothic,serif;\"><span style=\"font-size: large;\">\u00a0: Dans un triangle rectangle, le produit des mesures de l\u2019hypot\u00e9nuse et de la hauteur correspondante est \u00e9gal au produit des mesures des c\u00f4t\u00e9s de l\u2019angle droit.<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/section>\n","protected":false},"excerpt":{"rendered":"\u00c9NONC\u00c9S Les angles oppos\u00e9s par le sommet sont isom\u00e9triques. La somme des mesures des angles int\u00e9rieurs d\u2019un triangle est 180\u00b0. Si une s\u00e9cante coupe deux droites parall\u00e8les, alors les angles [correspondants, alternes-internes ou alternes-externes] sont isom\u00e9triques. Si deux angles correspondants, alternes-internes ou alternes-externes sont isom\u00e9triques, alors ils sont form\u00e9s par des droites parall\u00e8les coup\u00e9es par...","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1610","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pascal-tic.org\/math\/wp-json\/wp\/v2\/pages\/1610","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pascal-tic.org\/math\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pascal-tic.org\/math\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pascal-tic.org\/math\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pascal-tic.org\/math\/wp-json\/wp\/v2\/comments?post=1610"}],"version-history":[{"count":2,"href":"https:\/\/pascal-tic.org\/math\/wp-json\/wp\/v2\/pages\/1610\/revisions"}],"predecessor-version":[{"id":1615,"href":"https:\/\/pascal-tic.org\/math\/wp-json\/wp\/v2\/pages\/1610\/revisions\/1615"}],"wp:attachment":[{"href":"https:\/\/pascal-tic.org\/math\/wp-json\/wp\/v2\/media?parent=1610"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}