{"id":132,"date":"2022-04-13T08:26:25","date_gmt":"2022-04-13T08:26:25","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=132"},"modified":"2025-10-31T10:26:15","modified_gmt":"2025-10-31T10:26:15","slug":"h-4-proving-a-quadrilateral-is-a-parallelogram","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/h-4-proving-a-quadrilateral-is-a-parallelogram\/","title":{"rendered":"H.4 Proving a quadrilateral is a parallelogram"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Proving a quadrilateral is a parallelogram<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAG3Wj92cXc\/HSHE9qHeSD6a9zEgqzyzHw\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3Wj92cXc&#x2F;HSHE9qHeSD6a9zEgqzyzHw&#x2F;watch?utm_content=DAG3Wj92cXc&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">Design<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b;text-transform:capitalize\"><strong>key notes :<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-9b76e8a25c00b1eba1913ca6cdc6a823\" style=\"color:#000060\">\ud83d\udd39 <strong>Definition:<\/strong><\/h3>\n\n\n\n<p>A <strong>parallelogram<\/strong> is a <strong>quadrilateral<\/strong> (4-sided figure) where <strong>both pairs of opposite sides are parallel<\/strong>. \u27a1\ufe0f\u2b05\ufe0f<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-d70c747cf4faee8a88015f34d26ab933\" style=\"color:#000060\">\ud83d\udccf <strong>Ways to Prove a Quadrilateral is a Parallelogram:<\/strong><\/h3>\n\n\n\n<p>There are <strong>five main methods<\/strong> to prove that a quadrilateral is a parallelogram \ud83d\udc47<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-4cb4e720f10c9818d02400ec2adfa869\" style=\"color:#000060\">\ud83d\udfe9 <strong>Both pairs of opposite sides are parallel<\/strong><\/h3>\n\n\n\n<p>\u27a1\ufe0f AB \u2225 CD and AD \u2225 BC<br>\u2705 If <strong>both pairs<\/strong> of opposite sides are parallel, the quadrilateral is a parallelogram.<\/p>\n\n\n\n<p>\ud83e\udde0 <em>Example:<\/em> If in quadrilateral ABCD, AB \u2225 CD and AD \u2225 BC \u2192 ABCD is a parallelogram.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-6d2b8a3cf0327b84c4d3c8822d699ed2\" style=\"color:#000060\">\ud83d\udfe8 <strong>Both pairs of opposite sides are equal<\/strong><\/h3>\n\n\n\n<p>\ud83d\udccf AB = CD and AD = BC<br>\u2705 If both pairs of opposite sides are equal in length, it\u2019s a parallelogram.<\/p>\n\n\n\n<p>\ud83e\udde0 <em>Example:<\/em> If AB = CD and AD = BC \u2192 ABCD is a parallelogram.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-22b9f0e6f2d996e25b770813fd38f464\" style=\"color:#000060\">\ud83d\udfe6 <strong>One pair of opposite sides is both parallel and equal<\/strong><\/h3>\n\n\n\n<p>\u27a1\ufe0f AB \u2225 CD and AB = CD<br>\u2705 If one pair of opposite sides is <strong>parallel<\/strong> and <strong>equal in length<\/strong>, the quadrilateral is a parallelogram.<\/p>\n\n\n\n<p>\ud83e\udde0 <em>Example:<\/em> If AB \u2225 CD and AB = CD \u2192 ABCD is a parallelogram.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-38d35eeb21075dd8144fa0e1b8f1f8a9\" style=\"color:#000060\">\ud83d\udfe7 <strong>Both pairs of opposite angles are equal<\/strong><\/h3>\n\n\n\n<p>\ud83d\udd3a \u2220A = \u2220C and \u2220B = \u2220D<br>\u2705 If both pairs of opposite angles are equal, the quadrilateral is a parallelogram.<\/p>\n\n\n\n<p>\ud83e\udde0 <em>Example:<\/em> If \u2220A = \u2220C and \u2220B = \u2220D \u2192 ABCD is a parallelogram.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-29a50469c18c07d9e9c881d8730769ea\" style=\"color:#000060\">\ud83d\udfe5 <strong>The diagonals bisect each other<\/strong><\/h3>\n\n\n\n<p>\u2702\ufe0f AC and BD bisect each other at midpoint O<br>\u2705 If the diagonals of a quadrilateral <strong>bisect each other<\/strong>, the figure is a parallelogram.<\/p>\n\n\n\n<p>\ud83e\udde0 <em>Example:<\/em> If AO = OC and BO = OD \u2192 ABCD is a parallelogram.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-acaf984b8f4cda64fb6f0625a5194568\" style=\"color:#000060\">\ud83d\udca1 <strong>Remember:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Every <strong>rectangle, rhombus, and square<\/strong> is a <strong>parallelogram<\/strong> because they all satisfy these conditions. \ud83e\udde9<\/li>\n\n\n\n<li><strong>Coordinate Geometry Tip:<\/strong> You can use the <strong>slope formula<\/strong> or <strong>distance formula<\/strong> to verify parallelism or equality. \ud83d\udcd0<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-b0cd6732ff5bbccc684ed5b7c848557b\" style=\"color:#000060\">\ud83e\udded <strong>Quick Summary Table:<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Property<\/th><th>Condition<\/th><th>Result<\/th><\/tr><\/thead><tbody><tr><td>\ud83d\udd39 Opp. sides \u2225<\/td><td>Both pairs<\/td><td>Parallelogram<\/td><\/tr><tr><td>\ud83d\udd38 Opp. sides =<\/td><td>Both pairs<\/td><td>Parallelogram<\/td><\/tr><tr><td>\ud83d\udd3a 1 pair \u2225 &amp; =<\/td><td>One pair<\/td><td>Parallelogram<\/td><\/tr><tr><td>\ud83d\udd37 Opp. angles =<\/td><td>Both pairs<\/td><td>Parallelogram<\/td><\/tr><tr><td>\u2702\ufe0f Diagonals bisect<\/td><td>Each other<\/td><td>Parallelogram<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-20052fa6a1106899a379bbe6f54934e1\" style=\"color:#000060\">\ud83c\udf08 <strong>Fun Fact:<\/strong><\/h3>\n\n\n\n<p>All parallelograms are quadrilaterals, but not all quadrilaterals are parallelograms! \ud83d\ude09<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b0f4ad\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Can&nbsp;you show that this quadrilateral is a&nbsp;parallelogram?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-15.png\" alt=\"\" class=\"wp-image-8582\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-15.png 670w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-15-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>yes<\/li>\n\n\n\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>One pair of opposite angles measures 118\u00b0. Another angle measures 62\u00b0.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/Untitled_design__20_-removebg-preview-2.png\" alt=\"\" class=\"wp-image-11791\" style=\"aspect-ratio:3.35;width:539px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/Untitled_design__20_-removebg-preview-2.png 670w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/Untitled_design__20_-removebg-preview-2-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n\n\n\n<p>The quadrilateral is a parallelogram if the unlabeled angle also measures 62\u00b0. Call the unlabeled angle measure x. Set the sum of the interior angle measures equal to 360\u00b0 and solve for x.<\/p>\n\n\n\n<p>118\u00b0+62\u00b0+118\u00b0+x = 360\u00b0<\/p>\n\n\n\n<p>298\u00b0+x = 360\u00b0       Ad<\/p>\n\n\n\n<p>x = 62\u00b0              Subtract 298\u00b0 from both sides<\/p>\n\n\n\n<p>Since x=62\u00b0, both pairs of opposite angles are congruent. So, this quadrilateral is a parallelogram.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#c7e8eb\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Can&nbsp;you show that this quadrilateral is a&nbsp;parallelogram?<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph-the-square-with-vertices-\u2013-49-94-4-\u2013-9-and-\u2013-9-\u2013-4.-7.png\" alt=\"\" class=\"wp-image-8584\" style=\"width:336px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph-the-square-with-vertices-\u2013-49-94-4-\u2013-9-and-\u2013-9-\u2013-4.-7.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph-the-square-with-vertices-\u2013-49-94-4-\u2013-9-and-\u2013-9-\u2013-4.-7-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph-the-square-with-vertices-\u2013-49-94-4-\u2013-9-and-\u2013-9-\u2013-4.-7-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>yes<\/li>\n\n\n\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>One pair of opposite angles measures 69\u00b0. Another angle measures 111\u00b0.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph_the_square_with_vertices_____4_9____9_4____4____9__and_____9____4_.__7_-removebg-preview.png\" alt=\"\" class=\"wp-image-8585\" style=\"aspect-ratio:1;width:384px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph_the_square_with_vertices_____4_9____9_4____4____9__and_____9____4_.__7_-removebg-preview.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph_the_square_with_vertices_____4_9____9_4____4____9__and_____9____4_.__7_-removebg-preview-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph_the_square_with_vertices_____4_9____9_4____4____9__and_____9____4_.__7_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>The quadrilateral is a parallelogram if the unlabeled angle also measures 111\u00b0. Call the unlabeled angle measure x. Set the sum of the interior angle measures equal to 360\u00b0 and solve for x.<\/p>\n\n\n\n<p>69\u00b0+111\u00b0+69\u00b0+x = 360\u00b0<\/p>\n\n\n\n<p>249\u00b0+x = 360\u00b0               Add<\/p>\n\n\n\n<p>x = 111\u00b0                   Subtract 249\u00b0 from both sides<\/p>\n\n\n\n<p>Since x=111\u00b0, both pairs of opposite angles are congruent. So, this quadrilateral is a parallelogram.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#d1cbf9\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Can&nbsp;you show that this quadrilateral is a&nbsp;parallelogram?<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph-the-square-with-vertices-\u2013-49-94-4-\u2013-9-and-\u2013-9-\u2013-4.-8.png\" alt=\"\" class=\"wp-image-8587\" style=\"width:318px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph-the-square-with-vertices-\u2013-49-94-4-\u2013-9-and-\u2013-9-\u2013-4.-8.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph-the-square-with-vertices-\u2013-49-94-4-\u2013-9-and-\u2013-9-\u2013-4.-8-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph-the-square-with-vertices-\u2013-49-94-4-\u2013-9-and-\u2013-9-\u2013-4.-8-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>yes<\/li>\n\n\n\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Since&nbsp;one diagonal is split into non-congruent segments with length&nbsp;39&nbsp;and length&nbsp;38,&nbsp;the diagonals do not bisect each&nbsp;other.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph_the_square_with_vertices_____4_9____9_4____4____9__and_____9____4_.__8_-removebg-preview.png\" alt=\"\" class=\"wp-image-8589\" style=\"aspect-ratio:1;width:299px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph_the_square_with_vertices_____4_9____9_4____4____9__and_____9____4_.__8_-removebg-preview.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph_the_square_with_vertices_____4_9____9_4____4____9__and_____9____4_.__8_-removebg-preview-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Graph_the_square_with_vertices_____4_9____9_4____4____9__and_____9____4_.__8_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>So, the quadrilateral is not a parallelogram.<\/p>\n<\/div><\/div>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">\ud83c\udfcb\ufe0f\u200d\u2642\ufe0f Work it out\ud83c\udfcb\ufe0f\u200d\u2640\ufe0f<br><br>Not feeling ready yet? These can help:<br><br>\ud83e\udd4f<a href=\"https:\/\/9thclass.deltapublications.in\/index.php\/h-1-classify-quadrilaterals\/\" title=\"H.1 Classify quadrilaterals\"><\/a><a href=\"https:\/\/9thclass.deltapublications.in\/index.php\/h-3-properties-of-parallelograms\/\" title=\"H.3 Properties of parallelograms\">Properties of parallelograms<\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/84791\/382\/770\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-40.png\" alt=\"\" class=\"wp-image-7795\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-40.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-40-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-40-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/85170\/768\/831\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-49.png\" alt=\"\" class=\"wp-image-7796\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-49.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-49-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-49-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Proving a quadrilateral is a parallelogram Design by Delta publications key notes : \ud83d\udd39 Definition: A parallelogram is a quadrilateral (4-sided figure) where both pairs of opposite sides are parallel. \u27a1\ufe0f\u2b05\ufe0f \ud83d\udccf Ways to Prove a Quadrilateral is a Parallelogram: There are five main methods to prove that a quadrilateral is a parallelogram \ud83d\udc47 \ud83d\udfe9<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/h-4-proving-a-quadrilateral-is-a-parallelogram\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.4 Proving a quadrilateral is a parallelogram&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-132","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/132","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=132"}],"version-history":[{"count":27,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/132\/revisions"}],"predecessor-version":[{"id":18168,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/132\/revisions\/18168"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}