{"id":6689,"date":"2011-04-04T23:00:46","date_gmt":"2011-04-04T22:00:46","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6689"},"modified":"2022-01-17T18:16:27","modified_gmt":"2022-01-17T18:16:27","slug":"sabendo-que-3","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6689","title":{"rendered":"Sabendo que"},"content":{"rendered":"<p><ul id='GTTabs_ul_6689' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6689' class='GTTabs_curr'><a  id=\"6689_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6689' ><a  id=\"6689_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_6689'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span> <a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8Pag133-7.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6690\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6690\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8Pag133-7.jpg\" data-orig-size=\"598,288\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Tri\u00e2ngulos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8Pag133-7.jpg\" class=\"alignright size-full wp-image-6690\" title=\"Tri\u00e2ngulos\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8Pag133-7.jpg\" alt=\"\" width=\"359\" height=\"173\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8Pag133-7.jpg 598w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8Pag133-7-300x144.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8Pag133-7-150x72.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8Pag133-7-400x192.jpg 400w\" sizes=\"auto, (max-width: 359px) 100vw, 359px\" \/><\/a>Sabendo que:<\/p>\n<ul>\n<li>$[DE]\/\/[AB]$<\/li>\n<li>$\\overline{CD}=5\\,cm$<\/li>\n<li>$\\overline{DA}=3\\,cm$<\/li>\n<li>$\\overline{CE}=7\\,cm$<\/li>\n<\/ul>\n<ol>\n<li>Determina a raz\u00e3o de semelhan\u00e7a que transforma o tri\u00e2ngulo [DEC] no tri\u00e2ngulo [ABC].<\/li>\n<li>Calcula $\\overline{EB}$.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6689' onClick='GTTabs_show(1,6689)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6689'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Como os segmentos de reta [<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8Pag133-7.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6690\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6690\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8Pag133-7.jpg\" data-orig-size=\"598,288\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Tri\u00e2ngulos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8Pag133-7.jpg\" class=\"alignright size-full wp-image-6690\" title=\"Tri\u00e2ngulos\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8Pag133-7.jpg\" alt=\"\" width=\"359\" height=\"173\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8Pag133-7.jpg 598w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8Pag133-7-300x144.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8Pag133-7-150x72.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8Pag133-7-400x192.jpg 400w\" sizes=\"auto, (max-width: 359px) 100vw, 359px\" \/><\/a>DE] e [AB] s\u00e3o paralelos, ent\u00e3o os \u00e2ngulos CDE e CAB s\u00e3o geometricamente iguais, pois s\u00e3o \u00e2ngulos agudos de lados paralelos.<br \/>\nDe forma an\u00e1loga se conclui que tamb\u00e9m s\u00e3o geometricamente iguais os \u00e2ngulos CED e CBA.<br \/>\nLogo, os tri\u00e2ngulos [ABC] e [CDE] s\u00e3o semelhantes, pois possuem dois \u00e2ngulos geometricamente iguais, cada um a cada um, de um para o outro dos tri\u00e2ngulos.<\/p>\n<p>Assim, a raz\u00e3o de semelhan\u00e7a que transforma o tri\u00e2ngulo [DEC] no tri\u00e2ngulo [ABC] \u00e9: \\[r=\\frac{\\overline{CA}}{\\overline{CD}}=\\frac{5+3}{5}=\\frac{8}{5}=1,6\\]<\/p>\n<\/li>\n<li>Usando a raz\u00e3o de semelhan\u00e7a calculada na al\u00ednea anterior, ser\u00e1 $\\overline{CB}=r\\times \\overline{CE}$.<br \/>\nLogo, \\[\\overline{CB}=\\frac{8}{5}\\times 7=\\frac{56}{5}=11,2\\] Assim, $\\overline{EB}=\\overline{CB}-\\overline{EB}=11,2\\,cm-7\\,cm=4,2\\,cm$.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6689' onClick='GTTabs_show(0,6689)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sabendo que: $[DE]\/\/[AB]$ $\\overline{CD}=5\\,cm$ $\\overline{DA}=3\\,cm$ $\\overline{CE}=7\\,cm$ Determina a raz\u00e3o de semelhan\u00e7a que transforma o tri\u00e2ngulo [DEC] no tri\u00e2ngulo [ABC]. Calcula $\\overline{EB}$. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20514,"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-6689","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":2152,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8V1Pag133-7_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6689","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=6689"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6689\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20514"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6689"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6689"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6689"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6689"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}