{"id":14425,"date":"2018-04-12T22:17:12","date_gmt":"2018-04-12T21:17:12","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14425"},"modified":"2022-01-07T21:08:25","modified_gmt":"2022-01-07T21:08:25","slug":"um-quadrado-e-quatro-triangulos-geometricamente-iguais","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14425","title":{"rendered":"Um quadrado e quatro tri\u00e2ngulos geometricamente iguais"},"content":{"rendered":"<p><ul id='GTTabs_ul_14425' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14425' class='GTTabs_curr'><a  id=\"14425_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14425' ><a  id=\"14425_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_14425'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14426\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14426\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9.png\" data-orig-size=\"360,362\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Planifica\u00e7\u00e3o de pir\u00e2mide quadrangular\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9-298x300.png\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9.png\" class=\"alignright size-medium wp-image-14426\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9-298x300.png\" alt=\"\" width=\"298\" height=\"300\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9-298x300.png 298w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9-150x150.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9-160x160.png 160w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9.png 360w\" sizes=\"auto, (max-width: 298px) 100vw, 298px\" \/><\/a>Na figura, est\u00e3o representados um quadrado e quatro tri\u00e2ngulos geometricamente iguais.<br \/>\nEm cada um destes tri\u00e2ngulos:<\/p>\n<ul>\n<li>um dos lados \u00e9 tamb\u00e9m lado do quadrado;<\/li>\n<li>os outros dois lados s\u00e3o geometricamente iguais.<\/li>\n<\/ul>\n<ol>\n<li>Quantos eixos de simetria de reflex\u00e3o tem esta figura?<\/li>\n<li>A figura anterior \u00e9 uma planifica\u00e7\u00e3o de um s\u00f3lido.<br \/>\nRelativamente ao tri\u00e2ngulo [<em>ABF<\/em>], sabe-se que:<\/li>\n<\/ol>\n<ul>\n<li>a altura relativa \u00e0 base [<em>AB<\/em>] \u00e9 5;<\/li>\n<li>\\(\\overline {AB} = 6\\):<\/li>\n<\/ul>\n<p style=\"padding-left: 30px;\">Qual \u00e9 a altura deste s\u00f3lido?<br \/>\nCome\u00e7a por fazer um esbo\u00e7o do s\u00f3lido, a l\u00e1pis, e nele desenha o segmento de reta correspondente \u00e0 sua altura. Apresenta todos os c\u00e1lculos que efetuares.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14425' onClick='GTTabs_show(1,14425)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14425'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14426\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14426\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9.png\" data-orig-size=\"360,362\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Planifica\u00e7\u00e3o de pir\u00e2mide quadrangular\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9-298x300.png\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9.png\" class=\"alignright size-medium wp-image-14426\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9-298x300.png\" alt=\"\" width=\"298\" height=\"300\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9-298x300.png 298w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9-150x150.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9-160x160.png 160w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9.png 360w\" sizes=\"auto, (max-width: 298px) 100vw, 298px\" \/><\/a>A figura tem 4 eixos de simetria de reflex\u00e3o: as retas <em>AC<\/em>, <em>BD<\/em>, <em>EG<\/em> e <em>FH<\/em>.<br \/>\n\u00ad<\/li>\n<li>O s\u00f3lido considerado \u00e9 uma pir\u00e2mide quadrangular regular.<br \/>\nSeja <em>V<\/em> o v\u00e9rtice dessa pir\u00e2mide, <em>V&#8217;<\/em> o centro do quadrado [<em>ABCD<\/em>] e <em>M<\/em> o ponto m\u00e9dio de [<em>AB<\/em>].<br \/>\nO segmento de reta correspondente \u00e0 altura da pir\u00e2mide \u00e9 [<em>VV&#8217;<\/em>].<br \/>\nPor aplica\u00e7\u00e3o do Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [<em>MVV&#8217;<\/em>], temos:<br \/>\n\\[\\overline {VV&#8217;} = \\sqrt {{{\\overline {MV} }^2} &#8211; {{\\overline {MV&#8217;} }^2}} = \\sqrt {{5^2} &#8211; {3^2}} = 4\\]<\/li>\n<\/ol>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13488\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13488\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-3.png\" data-orig-size=\"270,220\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Pir\u00e2mide\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-3.png\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-3.png\" class=\"size-full wp-image-13488 aligncenter\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-3.png\" alt=\"\" width=\"270\" height=\"220\" \/><\/a><\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14425' onClick='GTTabs_show(0,14425)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura, est\u00e3o representados um quadrado e quatro tri\u00e2ngulos geometricamente iguais. Em cada um destes tri\u00e2ngulos: um dos lados \u00e9 tamb\u00e9m lado do quadrado; os outros dois lados s\u00e3o geometricamente iguais.&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14427,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,303],"tags":[426,306],"series":[],"class_list":["post-14425","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-equacoes-do-2-o-grau","tag-9-o-ano","tag-equacao-do-2-o-grau"],"views":2615,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag87-9a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14425","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=14425"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14425\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14427"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14425"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14425"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14425"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14425"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}