{"id":10784,"date":"2012-10-23T13:22:42","date_gmt":"2012-10-23T12:22:42","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=10784"},"modified":"2022-01-20T18:00:47","modified_gmt":"2022-01-20T18:00:47","slug":"cortes-produzidos-num-tetraedro","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=10784","title":{"rendered":"Cortes produzidos num tetraedro"},"content":{"rendered":"<p><ul id='GTTabs_ul_10784' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_10784' class='GTTabs_curr'><a  id=\"10784_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_10784' ><a  id=\"10784_1\" onMouseOver=\"GTTabsShowLinks('R1'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>R1<\/a><\/li>\n<li id='GTTabs_li_2_10784' ><a  id=\"10784_2\" onMouseOver=\"GTTabsShowLinks('R2'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>R2<\/a><\/li>\n<li id='GTTabs_li_3_10784' ><a  id=\"10784_3\" onMouseOver=\"GTTabsShowLinks('R3'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>R3<\/a><\/li>\n<li id='GTTabs_li_4_10784' ><a  id=\"10784_4\" onMouseOver=\"GTTabsShowLinks('R4'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>R4<\/a><\/li>\n<li id='GTTabs_li_5_10784' ><a  id=\"10784_5\" onMouseOver=\"GTTabsShowLinks('R5'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>R5<\/a><\/li>\n<li id='GTTabs_li_6_10784' ><a  id=\"10784_6\" onMouseOver=\"GTTabsShowLinks('R6'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>R6<\/a><\/li>\n<li id='GTTabs_li_7_10784' ><a  id=\"10784_7\" onMouseOver=\"GTTabsShowLinks('R7'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>R7<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_10784'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Seja [BDEG] um tetraedro regular.<\/p>\n<p>Os pontos M, N e Q s\u00e3o pontos m\u00e9dios das arestas a que pertencem.<\/p>\n<p>Desenhe os cortes produzidos no tetraedro pelos planos indicados.<\/p>\n<\/p>\n<table class=\" aligncenter\" style=\"width: 600px;\" border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Plano MNG<\/td>\n<td><\/td>\n<td style=\"text-align: center;\">Plano MNQ<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-1.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10794\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10794\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-1.jpg\" data-orig-size=\"265,238\" 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;}\" data-image-title=\"Tetraedro\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-1.jpg\" class=\"aligncenter  wp-image-10794\" title=\"Tetraedro\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-1.jpg\" alt=\"\" width=\"212\" height=\"190\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-1.jpg 265w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-1-150x134.jpg 150w\" sizes=\"auto, (max-width: 212px) 100vw, 212px\" \/><\/a><\/td>\n<td><\/td>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10795\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10795\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-2.jpg\" data-orig-size=\"265,238\" 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;}\" data-image-title=\"Tetraedro\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-2.jpg\" class=\"aligncenter  wp-image-10795\" title=\"Tetraedro\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-2.jpg\" alt=\"\" width=\"212\" height=\"190\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-2.jpg 265w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-2-150x134.jpg 150w\" sizes=\"auto, (max-width: 212px) 100vw, 212px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">Plano que cont\u00e9m a reta MN e \u00e9 paralelo a DG<\/td>\n<td><\/td>\n<td style=\"text-align: center;\">Plano MNT, sendo $\\overline {TG}\u00a0 = \\frac{1}{4}\\overline {BG} $<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-3.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10796\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10796\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-3.jpg\" data-orig-size=\"265,238\" 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;}\" data-image-title=\"Tetraedro\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-3.jpg\" class=\"aligncenter  wp-image-10796\" title=\"Tetraedro\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-3.jpg\" alt=\"\" width=\"212\" height=\"190\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-3.jpg 265w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-3-150x134.jpg 150w\" sizes=\"auto, (max-width: 212px) 100vw, 212px\" \/><\/a><\/td>\n<td><\/td>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-4.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10797\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10797\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-4.jpg\" data-orig-size=\"265,238\" 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;}\" data-image-title=\"Tetraedro\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-4.jpg\" class=\"aligncenter  wp-image-10797\" title=\"Tetraedro\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-4.jpg\" alt=\"\" width=\"212\" height=\"190\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-4.jpg 265w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-4-150x134.jpg 150w\" sizes=\"auto, (max-width: 212px) 100vw, 212px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">Plano que cont\u00e9m a reta UM e \u00e9 paralelo a DG<\/td>\n<td><\/td>\n<td style=\"text-align: center;\">Plano MBG<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-5.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10798\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10798\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-5.jpg\" data-orig-size=\"265,238\" 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;}\" data-image-title=\"Tetraedro\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-5.jpg\" class=\"aligncenter  wp-image-10798\" title=\"Tetraedro\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-5.jpg\" alt=\"\" width=\"212\" height=\"190\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-5.jpg 265w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-5-150x134.jpg 150w\" sizes=\"auto, (max-width: 212px) 100vw, 212px\" \/><\/a><\/td>\n<td><\/td>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-6.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10799\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10799\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-6.jpg\" data-orig-size=\"265,238\" 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;}\" data-image-title=\"Tetraedro\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-6.jpg\" class=\"aligncenter  wp-image-10799\" title=\"Tetraedro\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-6.jpg\" alt=\"\" width=\"212\" height=\"190\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-6.jpg 265w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-6-150x134.jpg 150w\" sizes=\"auto, (max-width: 212px) 100vw, 212px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" colspan=\"3\">Plano que passa em M e \u00e9 paralelo a DBG<\/td>\n<\/tr>\n<tr>\n<td colspan=\"3\">\u00a0<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-7.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10800\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10800\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-7.jpg\" data-orig-size=\"265,238\" 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;}\" data-image-title=\"Tetraedro\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-7.jpg\" class=\"aligncenter  wp-image-10800\" title=\"Tetraedro\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-7.jpg\" alt=\"\" width=\"212\" height=\"190\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-7.jpg 265w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/57-7-150x134.jpg 150w\" sizes=\"auto, (max-width: 212px) 100vw, 212px\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10784' onClick='GTTabs_show(1,10784)'>R1 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_10784'>\n<span class='GTTabs_titles'><b>R1<\/b><\/span><!--more--><\/p>\n<table border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Plano MNG<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57a-10-1.png\"><img loading=\"lazy\" decoding=\"async\" title=\"R1\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57a-10-1.png\" alt=\"\" width=\"271\" height=\"233\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td>O corte produzido \u00e9 o tri\u00e2ngulo is\u00f3sceles [MNG].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10784' onClick='GTTabs_show(0,10784)'>&lt;&lt; Enunciado<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10784' onClick='GTTabs_show(2,10784)'>R2 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_2_10784'>\n<span class='GTTabs_titles'><b>R2<\/b><\/span><\/p>\n<table border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Plano MNQ<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57b-10-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10813\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10813\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57b-10-1.png\" data-orig-size=\"838,817\" 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;}\" data-image-title=\"R2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57b-10-1.png\" class=\"aligncenter  wp-image-10813\" title=\"R2\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57b-10-1.png\" alt=\"\" width=\"302\" height=\"294\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57b-10-1.png 838w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57b-10-1-300x292.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57b-10-1-150x146.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57b-10-1-400x389.png 400w\" sizes=\"auto, (max-width: 302px) 100vw, 302px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td>O corte produzido \u00e9 o tri\u00e2ngulo equil\u00e1tero [MNQ].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10784' onClick='GTTabs_show(1,10784)'>&lt;&lt; R1<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10784' onClick='GTTabs_show(3,10784)'>R3 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_3_10784'>\n<span class='GTTabs_titles'><b>R3<\/b><\/span><\/p>\n<table border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Plano que cont\u00e9m a reta MN e \u00e9 paralelo a DG<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57c-10-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10814\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10814\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57c-10-1.png\" data-orig-size=\"829,784\" 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;}\" data-image-title=\"R3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57c-10-1.png\" class=\"aligncenter  wp-image-10814\" title=\"R3\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57c-10-1.png\" alt=\"\" width=\"298\" height=\"282\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57c-10-1.png 829w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57c-10-1-300x283.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57c-10-1-150x141.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57c-10-1-400x378.png 400w\" sizes=\"auto, (max-width: 298px) 100vw, 298px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td>\n<p>O corte produzido \u00e9 o quadrado [MNYX].<\/p>\n<p>$X \\in EG$ e $MX\\parallel DG$, $Y \\in BG$ e $NY\\parallel DG$.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10784' onClick='GTTabs_show(2,10784)'>&lt;&lt; R2<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10784' onClick='GTTabs_show(4,10784)'>R4 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_4_10784'>\n<span class='GTTabs_titles'><b>R4<\/b><\/span><\/p>\n<table border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Plano MNT, sendo $\\overline {TG}\u00a0 = \\frac{1}{4}\\overline {BG} $<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57d-10-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10815\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10815\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57d-10-1.png\" data-orig-size=\"809,788\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"R4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57d-10-1.png\" class=\"aligncenter  wp-image-10815\" title=\"R4\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57d-10-1.png\" alt=\"\" width=\"291\" height=\"284\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57d-10-1.png 809w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57d-10-1-300x292.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57d-10-1-150x146.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57d-10-1-400x389.png 400w\" sizes=\"auto, (max-width: 291px) 100vw, 291px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td>\n<p>O corte produzido \u00e9 o trap\u00e9zio is\u00f3sceles [MNTS].<\/p>\n<p>$S \\in EG$ e $ST\\parallel EB\\parallel MN$.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10784' onClick='GTTabs_show(3,10784)'>&lt;&lt; R3<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10784' onClick='GTTabs_show(5,10784)'>R5 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_5_10784'>\n<span class='GTTabs_titles'><b>R5<\/b><\/span><\/p>\n<table border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Plano que cont\u00e9m a reta UM e \u00e9 paralelo a DG<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57e-10-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10816\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10816\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57e-10-1.png\" data-orig-size=\"820,885\" 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;}\" data-image-title=\"R5\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57e-10-1.png\" class=\"aligncenter  wp-image-10816\" title=\"R5\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57e-10-1.png\" alt=\"\" width=\"295\" height=\"319\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57e-10-1.png 820w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57e-10-1-277x300.png 277w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57e-10-1-138x150.png 138w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57e-10-1-400x431.png 400w\" sizes=\"auto, (max-width: 295px) 100vw, 295px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td>\n<p>O corte produzido \u00e9 o quadril\u00e1tero [MUYX].<\/p>\n<p>$X \\in EG$ e $MX\\parallel DG$.<\/p>\n<p>O ponto $Y \\in BG$ determina-se obtendo primeiro o ponto I, ponto de intersec\u00e7\u00e3o das retas EB e UM.<\/p>\n<p>Y \u00e9 o ponto de intersec\u00e7\u00e3o de XI com BG.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10784' onClick='GTTabs_show(4,10784)'>&lt;&lt; R4<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10784' onClick='GTTabs_show(6,10784)'>R6 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_6_10784'>\n<span class='GTTabs_titles'><b>R6<\/b><\/span><\/p>\n<table border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Plano MBG<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57f-10-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10817\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10817\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57f-10-1.png\" data-orig-size=\"812,795\" 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;}\" data-image-title=\"R6\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57f-10-1.png\" class=\"aligncenter  wp-image-10817\" title=\"R6\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57f-10-1.png\" alt=\"\" width=\"292\" height=\"286\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57f-10-1.png 812w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57f-10-1-300x293.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57f-10-1-150x146.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57f-10-1-400x391.png 400w\" sizes=\"auto, (max-width: 292px) 100vw, 292px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td>O corte produzido \u00e9 o tri\u00e2ngulo is\u00f3sceles [MBG].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10784' onClick='GTTabs_show(5,10784)'>&lt;&lt; R5<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10784' onClick='GTTabs_show(7,10784)'>R7 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_7_10784'>\n<span class='GTTabs_titles'><b>R7<\/b><\/span><\/p>\n<table border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Plano que passa em M e \u00e9 paralelo a DBG<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57g-10-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10818\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10818\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57g-10-1.png\" data-orig-size=\"827,799\" 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;}\" data-image-title=\"R7\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57g-10-1.png\" class=\"aligncenter  wp-image-10818\" title=\"R7\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57g-10-1.png\" alt=\"\" width=\"298\" height=\"287\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57g-10-1.png 827w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57g-10-1-300x289.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57g-10-1-150x144.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/pag57g-10-1-400x386.png 400w\" sizes=\"auto, (max-width: 298px) 100vw, 298px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td>\n<p>O corte produzido \u00e9 o tri\u00e2ngulo\u00a0equil\u00e1tero [MXY].<\/p>\n<p>$X \\in EG$ e $MX\\parallel DG$.<\/p>\n<p>$Y \\in BE$ e $MY\\parallel BD$.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10784' onClick='GTTabs_show(6,10784)'>&lt;&lt; R6<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado R1 Enunciado Seja [BDEG] um tetraedro regular. Os pontos M, N e Q s\u00e3o pontos m\u00e9dios das arestas a que pertencem. Desenhe os cortes produzidos no tetraedro pelos planos indicados. Plano MNG Plano&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20753,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[321,97,334],"tags":[429,67,333],"series":[],"class_list":["post-10784","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-10-o-ano","category-aplicando","category-resolucao-de-problemas-de-geometria-no-plano-e-no-espaco","tag-10-o-ano","tag-geometria","tag-seccoes"],"views":3738,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/10V1Pag057-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10784","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=10784"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10784\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20753"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10784"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10784"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10784"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=10784"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}