{"id":4140,"date":"2010-10-18T15:06:32","date_gmt":"2010-10-18T14:06:32","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=4140"},"modified":"2022-01-18T23:29:52","modified_gmt":"2022-01-18T23:29:52","slug":"eixo-de-simetria-do-triangulo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=4140","title":{"rendered":"Eixo de simetria do tri\u00e2ngulo"},"content":{"rendered":"<p><ul id='GTTabs_ul_4140' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_4140' class='GTTabs_curr'><a  id=\"4140_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_4140' ><a  id=\"4140_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_4140'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p style=\"text-align: left;\">Observando a figura e sabendo que CM \u00e9 eixo de simetria do tri\u00e2ngulo [ABC], determina as amplitudes dos \u00e2ngulos e as medidas dos comprimentos dos lados do tri\u00e2ngulo.<\/p>\n<p style=\"text-align: left;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-7.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"4143\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=4143\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-7.jpg\" data-orig-size=\"618,256\" 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=\"Eixo de simetria\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-7.jpg\" class=\"aligncenter wp-image-4143\" title=\"Eixo de simetria\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-7-300x124.jpg\" alt=\"\" width=\"400\" height=\"166\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-7-300x124.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-7-150x62.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-7-400x165.jpg 400w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-7.jpg 618w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a><\/p>\n<p style=\"text-align: center;\">\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_4140' onClick='GTTabs_show(1,4140)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_4140'>\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\/pag95-7.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"4143\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=4143\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-7.jpg\" data-orig-size=\"618,256\" 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=\"Eixo de simetria\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-7.jpg\" class=\"alignright wp-image-4143\" title=\"Eixo de simetria\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-7-300x124.jpg\" alt=\"\" width=\"400\" height=\"166\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-7-300x124.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-7-150x62.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-7-400x165.jpg 400w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-7.jpg 618w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>Sendo a reta CM um eixo de simetria do tri\u00e2ngulo [ABC], ent\u00e3o:<\/p>\n<ul>\n<li>$\\widehat{B}=\\widehat{A}=30{}^\\text{o}$<\/li>\n<li>$\\overline{BC}=\\overline{AC}=4\\,cm$<\/li>\n<li>$\\overline{BM}=\\overline{AM}=3,4\\,cm$<\/li>\n<\/ul>\n<p>Determinando a amplitude do \u00e2ngulo ACB, vem: \\[\\begin{array}{*{35}{l}}<br \/>\nA\\widehat{C}B &amp; = &amp; 180{}^\\text{o}-(C\\widehat{A}B+C\\widehat{B}A)\u00a0 \\\\<br \/>\n{} &amp; = &amp; 180{}^\\text{o}-(30{}^\\text{o}+30{}^\\text{o})\u00a0 \\\\<br \/>\n{} &amp; = &amp; 120{}^\\text{o}\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Assim, temos:<\/p>\n<ul>\n<li>$\\overline{AC}=4\\,cm$<\/li>\n<li>$\\overline{BC}=4\\,cm$<\/li>\n<li>$\\overline{AB}=6,8\\,cm$<\/li>\n<li>$\\widehat{A}=30{}^\\text{o}$<\/li>\n<li>$\\widehat{B}=30{}^\\text{o}$<\/li>\n<li>$\\widehat{C}=120{}^\\text{o}$<\/li>\n<\/ul>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_4140' onClick='GTTabs_show(0,4140)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observando a figura e sabendo que CM \u00e9 eixo de simetria do tri\u00e2ngulo [ABC], determina as amplitudes dos \u00e2ngulos e as medidas dos comprimentos dos lados do tri\u00e2ngulo. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20621,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,102],"tags":[424,105,67,106],"series":[],"class_list":["post-4140","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","tag-triangulos"],"views":7979,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/7V2Pag095-7_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4140","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=4140"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4140\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20621"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4140"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=4140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}