{"id":4244,"date":"2010-10-18T23:18:36","date_gmt":"2010-10-18T22:18:36","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=4244"},"modified":"2022-01-19T00:08:42","modified_gmt":"2022-01-19T00:08:42","slug":"um-triangulo-isosceles","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=4244","title":{"rendered":"Um tri\u00e2ngulo is\u00f3sceles"},"content":{"rendered":"<p><ul id='GTTabs_ul_4244' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_4244' class='GTTabs_curr'><a  id=\"4244_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_4244' ><a  id=\"4244_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_4244'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag102-3.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"4245\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=4245\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag102-3.jpg\" data-orig-size=\"273,223\" 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\u00e2ngulo is\u00f3sceles\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag102-3.jpg\" class=\"wp-image-4245 size-full alignright\" title=\"Tri\u00e2ngulo is\u00f3sceles\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag102-3.jpg\" alt=\"\" width=\"273\" height=\"223\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag102-3.jpg 273w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag102-3-150x122.jpg 150w\" sizes=\"auto, (max-width: 273px) 100vw, 273px\" \/><\/a>No tri\u00e2ngulo is\u00f3sceles [MAR], $\\overline{RA}=\\overline{MA}$ e $\\hat{A}=50{}^\\text{o}$.<\/p>\n<p>Determina ${\\hat{R}}$ e ${\\hat{M}}$.<\/p>\n<p style=\"text-align: center;\">\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_4244' onClick='GTTabs_show(1,4244)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_4244'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag102-3.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"4245\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=4245\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag102-3.jpg\" data-orig-size=\"273,223\" 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\u00e2ngulo is\u00f3sceles\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag102-3.jpg\" class=\"alignright wp-image-4245 size-full\" title=\"Tri\u00e2ngulo is\u00f3sceles\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag102-3.jpg\" alt=\"\" width=\"273\" height=\"223\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag102-3.jpg 273w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag102-3-150x122.jpg 150w\" sizes=\"auto, (max-width: 273px) 100vw, 273px\" \/><\/a>Como a soma dos \u00e2ngulos internos de um tri\u00e2ngulo \u00e9 um \u00e2ngulo raso, vem: $\\hat{M}+\\hat{R}=180{}^\\text{o}-\\hat{A}=180{}^\\text{o}-50{}^\\text{o}=130{}^\\text{o}$.<\/p>\n<p>Num tri\u00e2ngulo, a lados geometricamente iguais op\u00f5em-se \u00e2ngulos geometricamente iguais. Ora, como $\\overline{RA}=\\overline{MA}$, ent\u00e3o $\\hat{M}=\\hat{R}$.<\/p>\n<p>Assim, $\\hat{M}=\\hat{R}=\\frac{130{}^\\text{o}}{2}=65{}^\\text{o}$.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_4244' onClick='GTTabs_show(0,4244)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado No tri\u00e2ngulo is\u00f3sceles [MAR], $\\overline{RA}=\\overline{MA}$ e $\\hat{A}=50{}^\\text{o}$. Determina ${\\hat{R}}$ e ${\\hat{M}}$. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20627,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,102],"tags":[424,105,67],"series":[],"class_list":["post-4244","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-do-espaco-ao-plano","tag-8-o-ano","tag-angulos","tag-geometria"],"views":1320,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/7V2Pag102-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4244","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=4244"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4244\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20627"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4244"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4244"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4244"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=4244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}