{"id":6685,"date":"2011-04-04T19:54:42","date_gmt":"2011-04-04T18:54:42","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6685"},"modified":"2022-01-05T22:38:15","modified_gmt":"2022-01-05T22:38:15","slug":"podemos-ou-nao-concluir-que-os-triangulos-sao-semelhantes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6685","title":{"rendered":"Podemos ou n\u00e3o concluir que os tri\u00e2ngulos s\u00e3o semelhantes?"},"content":{"rendered":"<p><ul id='GTTabs_ul_6685' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6685' class='GTTabs_curr'><a  id=\"6685_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6685' ><a  id=\"6685_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_6685'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Podemos ou n\u00e3o concluir que s\u00e3o semelhantes dois tri\u00e2ngulos [ABC] e [DEF] tais que:<\/p>\n<ol>\n<li>$\\hat{A}=60{}^\\text{o}$, $\\hat{B}=70{}^\\text{o}$ e $\\hat{D}=50{}^\\text{o}$, $\\hat{E}=70{}^\\text{o}$?<\/li>\n<li>$\\overline{AB}=6\\,cm$, $\\overline{AC}=4\\,cm$ e $\\overline{DE}=12\\,cm$, $\\overline{DF}=8\\,cm$?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6685' onClick='GTTabs_show(1,6685)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6685'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Se $\\hat{A}=60{}^\\text{o}$ e $\\hat{B}=70{}^\\text{o}$, ent\u00e3o $\\hat{C}=180{}^\\text{o}-(\\hat{A}+\\hat{B})=180{}^\\text{o}-(60{}^\\text{o}+70{}^\\text{o})=50{}^\\text{o}$.\n<p>Tamb\u00e9m, se $\\hat{D}=50{}^\\text{o}$ e $\\hat{E}=70{}^\\text{o}$, ent\u00e3o $\\hat{F}=180{}^\\text{o}-(\\hat{D}+\\hat{E})=180{}^\\text{o}-(50{}^\\text{o}+70{}^\\text{o})=60{}^\\text{o}$.<\/p>\n<p>Portanto, os tri\u00e2ngulos\u00a0\u00a0[ABC] e [DEF] s\u00e3o semelhantes, pois possuem dois \u00e2ngulos geometricamente iguais, cada um a cada um, de um para o outro dos tri\u00e2ngulos.<\/p>\n<\/li>\n<li>Nada se pode concluir sobre a semelhan\u00e7a ou n\u00e3o dos tri\u00e2ngulos, pois os dados conhecidos s\u00e3o insuficientes para apurar se se verifica algum dos cit\u00e9rios de semelhan\u00e7a de tri\u00e2ngulos.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6685' onClick='GTTabs_show(0,6685)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Podemos ou n\u00e3o concluir que s\u00e3o semelhantes dois tri\u00e2ngulos [ABC] e [DEF] tais que: $\\hat{A}=60{}^\\text{o}$, $\\hat{B}=70{}^\\text{o}$ e $\\hat{D}=50{}^\\text{o}$, $\\hat{E}=70{}^\\text{o}$? $\\overline{AB}=6\\,cm$, $\\overline{AC}=4\\,cm$ e $\\overline{DE}=12\\,cm$, $\\overline{DF}=8\\,cm$? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14103,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,151],"tags":[149],"series":[],"class_list":["post-6685","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-semelhanca-de-triangulos-8--ano","tag-semelhanca-de-triangulos"],"views":2822,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat48.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6685","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6685"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6685\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14103"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6685"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6685"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6685"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6685"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}