{"id":128,"date":"2022-04-13T08:25:42","date_gmt":"2022-04-13T08:25:42","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=128"},"modified":"2025-10-24T06:53:01","modified_gmt":"2025-10-24T06:53:01","slug":"h-2-graph-quadrilaterals","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/h-2-graph-quadrilaterals\/","title":{"rendered":"H.2 Graph quadrilaterals"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Graph quadrilaterals<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\"><strong>Key Notes:<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd39 <strong>What is a Quadrilateral?<\/strong><\/h3>\n\n\n\n<p>\ud83d\udc49 A <strong>quadrilateral<\/strong> is a polygon with <strong>4 sides and 4 vertices (corners)<\/strong>.<br>\ud83d\udc49 The <strong>sum of all interior angles<\/strong> of a quadrilateral is <strong>360\u00b0<\/strong>. \ud83d\udd3a\u2795\ud83d\udd3b<\/p>\n\n\n\n<p>\ud83d\udfea Examples:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Square \u2b1c<\/li>\n\n\n\n<li>Rectangle \ud83d\udfe6<\/li>\n\n\n\n<li>Parallelogram \ud83d\udfe9<\/li>\n\n\n\n<li>Rhombus \ud83d\udc8e<\/li>\n\n\n\n<li>Trapezium \u23f9\ufe0f<\/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-large-font-size\">\ud83d\udd39 <strong>Coordinate Plane Basics<\/strong> \ud83e\udded<\/h3>\n\n\n\n<p>\ud83d\udc49 The <strong>coordinate plane<\/strong> has two axes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>x-axis (horizontal)<\/strong><\/li>\n\n\n\n<li><strong>y-axis (vertical)<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udccd Any point is represented as <strong>(x, y)<\/strong> \u2014 called an <strong>ordered pair<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd39 <strong>Plotting the Vertices<\/strong> \u270f\ufe0f<\/h3>\n\n\n\n<p>\ud83d\udc49 To graph a quadrilateral, <strong>plot all four vertices<\/strong> on the coordinate plane.<br>\ud83d\udc49 Example:<br>Let the vertices be A(1,2), B(5,2), C(5,5), D(1,5).<br>\ud83d\udcca Plot them carefully on the grid and connect the points in order \u2014 it forms a <strong>rectangle<\/strong>! \ud83d\udfe6<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd39 <strong>Connecting the Points<\/strong> \ud83d\udd17<\/h3>\n\n\n\n<p>\ud83e\udde9 After plotting, <strong>join the points in sequence<\/strong> \u2014 A\u2192B\u2192C\u2192D\u2192A \u2014 to form a <strong>closed figure<\/strong>.<br>\ud83d\udca1 Make sure the figure starts and ends at the same point!<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd39 <strong>Checking the Type of Quadrilateral<\/strong> \ud83e\uddee<\/h3>\n\n\n\n<p>You can determine the <strong>type<\/strong> of quadrilateral by using:<br>\u2705 <strong>Distance formula:<\/strong> to find side lengths <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"283\" height=\"47\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/10\/image-1.png\" alt=\"\" class=\"wp-image-17993\"\/><\/figure><\/div>\n\n\n<p>\u2705 <strong>Slope formula:<\/strong> to check if sides are parallel <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>m = y<sub>2<\/sub> \u2212 y<sub>1<\/sub> \/ x<sub>2<\/sub> &#8211; x<sub>1<\/sub><\/strong><\/p>\n\n\n\n<p>\u2705 <strong>Midpoint formula:<\/strong> to verify diagonals bisect each other <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"254\" height=\"72\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/10\/image-2.png\" alt=\"\" class=\"wp-image-17994\"\/><\/figure><\/div>\n\n\n<p>\ud83d\udccf Example: If opposite sides are <strong>equal and parallel<\/strong>, it\u2019s a <strong>parallelogram<\/strong>! \ud83d\udfe9<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd39 <strong>Identify the Shape by Properties<\/strong> \ud83e\udde0<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Quadrilateral<\/th><th>Properties<\/th><\/tr><\/thead><tbody><tr><td>\ud83d\udfe6 <strong>Rectangle<\/strong><\/td><td>Opposite sides equal &amp; parallel; angles 90\u00b0<\/td><\/tr><tr><td>\ud83d\udc8e <strong>Rhombus<\/strong><\/td><td>All sides equal; diagonals bisect at right angles<\/td><\/tr><tr><td>\u2b1c <strong>Square<\/strong><\/td><td>All sides equal; all angles 90\u00b0<\/td><\/tr><tr><td>\u23f9\ufe0f <strong>Trapezium<\/strong><\/td><td>Only one pair of opposite sides parallel<\/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-large-font-size\">\ud83d\udd39 <strong>Real-Life Applications<\/strong> \ud83c\udf0d<\/h3>\n\n\n\n<p>\ud83d\udcd0 Used in:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Designing buildings and floors \ud83c\udfe0<\/li>\n\n\n\n<li>Computer graphics &amp; animation \ud83d\udcbb<\/li>\n\n\n\n<li>Map plotting and architecture \ud83d\uddfa\ufe0f<\/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-large-font-size\">\ud83c\udf1f <strong>Summary:<\/strong><\/h3>\n\n\n\n<p>\ud83d\udc49 Plot the points \u27a1\ufe0f Connect them \u27a1\ufe0f Identify the shape \u27a1\ufe0f Verify with formulas!<br>\ud83d\udcaa Mastering graphing quadrilaterals helps in geometry, algebra, and real-world design. \ud83c\udfa8\ud83d\udcc8<\/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:#d0ddf4\"><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>Graph the parallelogram with vertices (8,\u20137), (\u20132,\u20137), (0,5) and (10,5).<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"602\" height=\"569\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.1.jpg\" alt=\"\" class=\"wp-image-11801\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.1.jpg 602w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.1-300x284.jpg 300w\" sizes=\"auto, (max-width: 602px) 100vw, 602px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>Graph the point (8,\u20137). Start at (0, 0). Move 8 units right and 7 units down.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"594\" height=\"573\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.2.jpg\" alt=\"\" class=\"wp-image-11802\" style=\"width:386px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.2.jpg 594w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.2-300x289.jpg 300w\" sizes=\"auto, (max-width: 594px) 100vw, 594px\" \/><\/figure><\/div>\n\n\n<p>To draw one side of the parallelogram, graph the point (\u20132,\u20137).<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"595\" height=\"578\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.3.jpg\" alt=\"\" class=\"wp-image-11803\" style=\"width:397px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.3.jpg 595w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.3-300x291.jpg 300w\" sizes=\"auto, (max-width: 595px) 100vw, 595px\" \/><\/figure><\/div>\n\n\n<p>To draw another side of the parallelogram, graph the point (0,5).<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"587\" height=\"567\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.4.jpg\" alt=\"\" class=\"wp-image-11804\" style=\"width:411px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.4.jpg 587w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.4-300x290.jpg 300w\" sizes=\"auto, (max-width: 587px) 100vw, 587px\" \/><\/figure><\/div>\n\n\n<p>To complete the parallelogram, graph the point (10,5).<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"606\" height=\"571\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.5.jpg\" alt=\"\" class=\"wp-image-11805\" style=\"width:422px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.5.jpg 606w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.5-300x283.jpg 300w\" sizes=\"auto, (max-width: 606px) 100vw, 606px\" \/><\/figure><\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#ebdaee\"><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 has-large-font-size\"><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>Graph the quadrilateral with vertices (\u20134,8),  (\u20136,\u20133), (3,8) and (0,7).<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"598\" height=\"570\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.6.jpg\" alt=\"\" class=\"wp-image-11806\" style=\"width:445px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.6.jpg 598w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.6-300x286.jpg 300w\" sizes=\"auto, (max-width: 598px) 100vw, 598px\" \/><\/figure><\/div><\/div><\/div>\n\n\n\n<p>Graph the point (4,8). Start at (0, 0). Move 4 units left and 8 units up.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"596\" height=\"576\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.7.jpg\" alt=\"\" class=\"wp-image-11807\" style=\"width:439px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.7.jpg 596w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.7-300x290.jpg 300w\" sizes=\"auto, (max-width: 596px) 100vw, 596px\" \/><\/figure><\/div>\n\n\n<p>To draw one side of the quadrilateral, graph the point (\u20136,\u20133).<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"596\" height=\"574\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.8.jpg\" alt=\"\" class=\"wp-image-11808\" style=\"width:441px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.8.jpg 596w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.8-300x289.jpg 300w\" sizes=\"auto, (max-width: 596px) 100vw, 596px\" \/><\/figure><\/div>\n\n\n<p>To draw another side of the quadrilateral, graph the point (3,8).<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"609\" height=\"572\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.9.jpg\" alt=\"\" class=\"wp-image-11809\" style=\"width:450px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.9.jpg 609w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/4.9-300x282.jpg 300w\" sizes=\"auto, (max-width: 609px) 100vw, 609px\" \/><\/figure><\/div>\n\n\n<p>To complete the quadrilateral, graph the point (0,7).<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"592\" height=\"569\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/5.jpg\" alt=\"\" class=\"wp-image-11810\" style=\"width:444px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/5.jpg 592w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/5-300x288.jpg 300w\" sizes=\"auto, (max-width: 592px) 100vw, 592px\" \/><\/figure><\/div><\/div><\/div>\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\/85128\/629\/814\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-42.png\" alt=\"\" class=\"wp-image-7804\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-42.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-42-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-42-150x150.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\"><div class=\"wp-block-image\">\n<figure class=\"alignright size-full is-resized\"><a href=\"https:\/\/wordwall.net\/play\/85167\/637\/958\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-51.png\" alt=\"\" class=\"wp-image-7802\" style=\"width:304px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-51.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-51-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-51-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure><\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Graph quadrilaterals Key Notes: \ud83d\udd39 What is a Quadrilateral? \ud83d\udc49 A quadrilateral is a polygon with 4 sides and 4 vertices (corners).\ud83d\udc49 The sum of all interior angles of a quadrilateral is 360\u00b0. \ud83d\udd3a\u2795\ud83d\udd3b \ud83d\udfea Examples: \ud83d\udd39 Coordinate Plane Basics \ud83e\udded \ud83d\udc49 The coordinate plane has two axes: \ud83d\udccd Any point is represented as (x,<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/h-2-graph-quadrilaterals\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.2 Graph quadrilaterals&#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-128","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/128","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=128"}],"version-history":[{"count":23,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/128\/revisions"}],"predecessor-version":[{"id":18135,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/128\/revisions\/18135"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}