{"id":4700,"date":"2010-10-27T16:47:20","date_gmt":"2010-10-27T15:47:20","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=4700"},"modified":"2022-01-19T12:45:20","modified_gmt":"2022-01-19T12:45:20","slug":"propriedades-dos-paralelogramos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=4700","title":{"rendered":"Propriedades dos paralelogramos"},"content":{"rendered":"<p><ul id='GTTabs_ul_4700' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_4700' class='GTTabs_curr'><a  id=\"4700_0\" onMouseOver=\"GTTabsShowLinks('Paralelogramos'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Paralelogramos<\/a><\/li>\n<li id='GTTabs_li_1_4700' ><a  id=\"4700_1\" onMouseOver=\"GTTabsShowLinks('Propriedades'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Propriedades<\/a><\/li>\n<li id='GTTabs_li_2_4700' ><a  id=\"4700_2\" onMouseOver=\"GTTabsShowLinks('Eixos de simetria'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Eixos de simetria<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_4700'>\n<span class='GTTabs_titles'><b>Paralelogramos<\/b><\/span><\/p>\n<p>H\u00e1 quadril\u00e1teros que n\u00e3o t\u00eam lados paralelos (N\u00e3o trap\u00e9zios), outros que t\u00eam dois lados paralelos (Trap\u00e9zios)\u00a0e outros que t\u00eam os lados paralelos dois a dois. Estes \u00faltimos s\u00e3o os <strong>paralelogramos<\/strong>.<\/p>\n<blockquote>\n<p><strong>Paralelogramos<\/strong> s\u00e3o quadril\u00e1teros com dois pares de lados paralelos, isto \u00e9, t\u00eam os lados paralelos dois a dois.<\/p>\n<\/blockquote>\n<p>Pelas suas caracter\u00edsticas particulares, no grupo dos quadril\u00e1teros paralelogramos podemos distinguir: o <strong>paralelogramo<\/strong> (propriamente dito), o <strong>ret\u00e2ngulo<\/strong>, o <strong>losango<\/strong> e o <strong>quadrado<\/strong>. Explora a anima\u00e7\u00e3o seguinte, de forma a recordares (ou descobrires) as diversas propriedades de cada um deles, relativamente aos \u00e2ngulos, lados, diagonais e eixos de simetria:<br \/>\n\u00ad<\/p>\n<p style=\"text-align: center;\"><script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":720,\r\n\"height\":463,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 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is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 0,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet')};\r\n<\/script><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_4700' onClick='GTTabs_show(1,4700)'>Propriedades &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_4700'>\n<span class='GTTabs_titles'><b>Propriedades<\/b><\/span><!--more--><\/p>\n<p>Consideremos o paralelogramo [ABCD]:<\/p>\n<p style=\"text-align: center;\"><div id=\"ggbApplet2\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet2\",\r\n\"width\":563,\r\n\"height\":282,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6\",\r\n\"showToolBarHelp\":false,\r\n\"showResetIcon\":true,\r\n\"enableLabelDrags\":false,\r\n\"enableShiftDragZoom\":false,\r\n\"enableRightClick\":false,\r\n\"errorDialogsActive\":false,\r\n\"useBrowserForJS\":false,\r\n\"preventFocus\":false,\r\n\"showFullscreenButton\":true,\r\n\"language\":\"pt\",\r\n\/\/ use this instead of ggbBase64 to load a material from GeoGebraTube\r\n\/\/ \"material_id\":12345,\r\n\"ggbBase64\":\"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is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 0,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet2 = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet'); applet2.inject('ggbApplet2')};\r\n<\/script><\/p>\n<p>Se considerarmos a diagonal [AC], o paralelogramo fica dividido em dois tri\u00e2ngulos geometricamente iguais (ALA), porque:<\/p>\n<ul>\n<li>t\u00eam um lado comum: [AC];<\/li>\n<li>$B\\hat{A}C=D\\hat{C}A$ e $C\\hat{A}D=A\\hat{C}B$, pois s\u00e3o amplitudes de dois \u00e2ngulos agudos (ou obtusos) de lados paralelos.<\/li>\n<\/ul>\n<p>Logo, $\\overline{AB}=\\overline{DC}$ e $\\overline{AD}=\\overline{BC}$.<\/p>\n<blockquote>\n<p><strong>Os lados opostos de um paralelogramo t\u00eam o mesmo comprimento.<\/strong><\/p>\n<\/blockquote>\n<p>Por outro lado,<\/p>\n<ul>\n<li>$A\\hat{B}C=A\\hat{D}C$, porque s\u00e3o amplitudes de \u00e2ngulos obtusos (ou agudos) de lados paralelos;<\/li>\n<li>$D\\hat{A}B=D\\hat{C}B$, porque s\u00e3o amplitudes de \u00e2ngulos agudos (ou obtusos) de lados paralelos.<\/li>\n<\/ul>\n<blockquote>\n<p><strong>Os \u00e2ngulos opostos de um paralelogramo t\u00eam a mesma amplitude.<\/strong><\/p>\n<\/blockquote>\n<p>\u00ad<br \/>\nTracemos agora as diagonais [AC] e [DB]. Elas intersectam-se no ponto O.<\/p>\n<p style=\"text-align: center;\"><div id=\"ggbApplet3\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet3\",\r\n\"width\":563,\r\n\"height\":282,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6\",\r\n\"showToolBarHelp\":false,\r\n\"showResetIcon\":true,\r\n\"enableLabelDrags\":false,\r\n\"enableShiftDragZoom\":false,\r\n\"enableRightClick\":false,\r\n\"errorDialogsActive\":false,\r\n\"useBrowserForJS\":false,\r\n\"preventFocus\":false,\r\n\"showFullscreenButton\":true,\r\n\"language\":\"pt\",\r\n\/\/ use this instead of ggbBase64 to load a material from GeoGebraTube\r\n\/\/ 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is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 0,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet3 = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet'); applet2.inject('ggbApplet2'); applet3.inject('ggbApplet3')};\r\n<\/script><\/p>\n<p>Os tri\u00e2ngulos [ABO] e [DCO] s\u00e3o geometricamente iguais (), pois<\/p>\n<ul>\n<li>$O\\hat{A}B=D\\hat{C}O$ e $A\\hat{B}O=C\\hat{D}O$, porque s\u00e3o as amplitudes de \u00e2ngulos agudos (ou obtusos) de lados paralelos;<\/li>\n<li>$\\overline{AB}=\\overline{DC}$, pois [AB] e [DC] s\u00e3o lados opostos do paralelogramo.<\/li>\n<\/ul>\n<p>Logo, $\\overline{AO}=\\overline{OC}$ e $\\overline{DO}=\\overline{OB}$.<\/p>\n<blockquote>\n<p><strong>As diagonais de um paralelogramo bissetam-se, isto \u00e9, dividem-se ao meio.<\/strong><\/p>\n<\/blockquote>\n<p>Podemos ainda provar (Como?) que<\/p>\n<blockquote>\n<p><strong>Dois \u00e2ngulos consecutivos de um paralelogramo s\u00e3o suplementares.<\/strong><\/p>\n<\/blockquote>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_4700' onClick='GTTabs_show(0,4700)'>&lt;&lt; Paralelogramos<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_4700' onClick='GTTabs_show(2,4700)'>Eixos de simetria &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_2_4700'>\n<span class='GTTabs_titles'><b>Eixos de simetria<\/b><\/span><\/p>\n<p>Estuda os eixos de simetria nos quadril\u00e1teros paralelogramos:<\/p>\n<\/p>\n<p style=\"text-align: center;\"><div id=\"ggbApplet4\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet4\",\r\n\"width\":720,\r\n\"height\":463,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6\",\r\n\"showToolBarHelp\":false,\r\n\"showResetIcon\":true,\r\n\"enableLabelDrags\":false,\r\n\"enableShiftDragZoom\":false,\r\n\"enableRightClick\":false,\r\n\"errorDialogsActive\":false,\r\n\"useBrowserForJS\":false,\r\n\"preventFocus\":false,\r\n\"showFullscreenButton\":true,\r\n\"language\":\"pt\",\r\n\/\/ use this instead of ggbBase64 to load a material from GeoGebraTube\r\n\/\/ 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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=\"Eixos de simetria\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/cdsdcds2.jpg\" class=\"aligncenter wp-image-4741 size-full\" title=\"Eixos de simetria\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/cdsdcds2.jpg\" alt=\"\" width=\"520\" height=\"266\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/cdsdcds2.jpg 520w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/cdsdcds2-300x153.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/cdsdcds2-150x76.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/cdsdcds2-400x204.jpg 400w\" sizes=\"auto, (max-width: 520px) 100vw, 520px\" \/><\/a><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_4700' onClick='GTTabs_show(1,4700)'>&lt;&lt; Propriedades<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Paralelogramos Propriedades Paralelogramos H\u00e1 quadril\u00e1teros que n\u00e3o t\u00eam lados paralelos (N\u00e3o trap\u00e9zios), outros que t\u00eam dois lados paralelos (Trap\u00e9zios)\u00a0e outros que t\u00eam os lados paralelos dois a dois. Estes \u00faltimos s\u00e3o os paralelogramos. 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