{"id":4049,"date":"2010-10-18T01:44:22","date_gmt":"2010-10-18T00:44:22","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=4049"},"modified":"2022-01-18T23:01:47","modified_gmt":"2022-01-18T23:01:47","slug":"um-tetraedro","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=4049","title":{"rendered":"Um tetraedro"},"content":{"rendered":"<p><ul id='GTTabs_ul_4049' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_4049' class='GTTabs_curr'><a  id=\"4049_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_4049' ><a  id=\"4049_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_4049'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag87-7.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"4052\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=4052\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag87-7.jpg\" data-orig-size=\"304,321\" 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=\"Tetraedro\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag87-7.jpg\" class=\"alignright wp-image-4052\" title=\"Tetraedro\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag87-7.jpg\" alt=\"\" width=\"240\" height=\"253\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag87-7.jpg 304w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag87-7-284x300.jpg 284w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag87-7-142x150.jpg 142w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Na figura est\u00e1 representado um tetraedro.<\/p>\n<ol>\n<li>Existem planos paralelos? E retas paralelas?<\/li>\n<li>Indica um plano que contenha a reta AD.<\/li>\n<li>Indica duas retas concorrentes.<\/li>\n<li>Est\u00e1 assinalado na figura um ponto que pertence a todas as faces laterais do tetraedro. Qual \u00e9 esse ponto?<\/li>\n<li>Indica dois planos concorrentes e diz qual \u00e9 a intersec\u00e7\u00e3o desses planos.<\/li>\n<li>Indica duas retas n\u00e3o complanares.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_4049' onClick='GTTabs_show(1,4049)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_4049'>\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\/2010\/10\/pag87-7.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"4052\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=4052\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag87-7.jpg\" data-orig-size=\"304,321\" 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=\"Tetraedro\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag87-7.jpg\" class=\"alignright wp-image-4052\" title=\"Tetraedro\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag87-7.jpg\" alt=\"\" width=\"240\" height=\"253\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag87-7.jpg 304w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag87-7-284x300.jpg 284w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag87-7-142x150.jpg 142w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>N\u00e3o existem planos paralelos, nem retas paralelas (utilizando exclusivamente letras da figura).<br \/>\n\u00ad<\/li>\n<li>Um plano que cont\u00e9m a reta AD \u00e9 o plano ABD (ou ACD).<br \/>\n\u00ad<\/li>\n<li>S\u00e3o concorrentes as retas BC e AC (ou AB e AD), por exemplo.<br \/>\n\u00ad<\/li>\n<li>O ponto que pertence a todas as faces laterais do tetraedro \u00e9 o ponto A.<br \/>\n\u00ad<\/li>\n<li>S\u00e3o concorrentes, por exemplo, os planos BCD e ABD; a intersec\u00e7\u00e3o desses planos \u00e9 a reta BD.<br \/>\nOutro exemplo: S\u00e3o concorrentes os planos ACD e ABC; a intersec\u00e7\u00e3o desses planos \u00e9 a reta AC.<br \/>\n\u00ad<\/li>\n<li>S\u00e3o n\u00e3o complanares, por exemplo, os seguintes pares de retas: AC e BD, BC e AD; CD e AB.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_4049' onClick='GTTabs_show(0,4049)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura est\u00e1 representado um tetraedro. Existem planos paralelos? E retas paralelas? Indica um plano que contenha a reta AD. Indica duas retas concorrentes. Est\u00e1 assinalado na figura um ponto que&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20617,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,102],"tags":[424,67,104,103],"series":[],"class_list":["post-4049","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-geometria","tag-poliedros","tag-solidos"],"views":2885,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/7V2Pag087-7_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4049","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=4049"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4049\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20617"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4049"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4049"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4049"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=4049"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}