{"id":138,"date":"2022-04-13T08:27:17","date_gmt":"2022-04-13T08:27:17","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=138"},"modified":"2025-11-01T04:57:34","modified_gmt":"2025-11-01T04:57:34","slug":"h-7-properties-of-trapeziums","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/h-7-properties-of-trapeziums\/","title":{"rendered":"H.7 Properties of trapeziums"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Properties of trapeziums<\/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 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\/DAG3bHgqeaE\/PmmeIa39PoZfCFFzpqbsSg\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3bHgqeaE&#x2F;PmmeIa39PoZfCFFzpqbsSg&#x2F;watch?utm_content=DAG3bHgqeaE&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<\/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<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-c80684906e2fc7b31b3f8c445532f0bd\" style=\"color:#000060\">\ud83d\udfe6 <strong>\ud83d\udd39 What is a Trapezium?<\/strong><\/h2>\n\n\n\n<p>A <strong>trapezium<\/strong> (also called a <strong>trapezoid<\/strong>) is a <strong>quadrilateral<\/strong> with <strong>one pair of parallel sides<\/strong>.<br>\ud83d\udc49 The <strong>parallel sides<\/strong> are called <strong>bases<\/strong>, and the <strong>non-parallel sides<\/strong> are called <strong>legs<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-5c114ed29fe4a9a17012bbb783c0945b\" style=\"color:#000060\">\ud83d\udfe9 <strong>\ud83d\udd39 Basic Properties of a Trapezium<\/strong><\/h2>\n\n\n\n<p>1\ufe0f\u20e3 <strong>One Pair of Parallel Sides<\/strong> \u27a1\ufe0f Only one pair of opposite sides are parallel.<br>2\ufe0f\u20e3 <strong>Sum of Interior Angles = 360\u00b0<\/strong> \ud83d\udd04<br>3\ufe0f\u20e3 <strong>Non-parallel sides (legs)<\/strong> can be <strong>equal or unequal<\/strong> in length.<br>4\ufe0f\u20e3 The <strong>diagonals<\/strong> usually <strong>are not equal<\/strong> and <strong>don\u2019t bisect<\/strong> each other (except in special types).<br>5\ufe0f\u20e3 The <strong>line joining midpoints<\/strong> of the non-parallel sides is <strong>parallel to the bases<\/strong> and <strong>half the sum of the lengths of the bases<\/strong>. \u2797<\/p>\n\n\n\n<p>\ud83e\uddee Formula:<br>\ud83d\udc49 Mid-segment = \u00bd \u00d7 (Base\u2081 + Base\u2082)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-9065fa4009b367285add76f057a85520\" style=\"color:#000060\">\ud83d\udfe7 <strong>\ud83d\udd39 Types of Trapeziums<\/strong><\/h2>\n\n\n\n<p>1\ufe0f\u20e3 <strong>Isosceles Trapezium<\/strong><br>\u2728 Non-parallel sides are <strong>equal<\/strong> in length.<br>\u2728 <strong>Base angles<\/strong> are <strong>equal<\/strong>.<br>\u2728 <strong>Diagonals are equal<\/strong> in length.<\/p>\n\n\n\n<p>2\ufe0f\u20e3 <strong>Right-Angled Trapezium<\/strong><br>\ud83d\udff0 Has <strong>two right angles (90\u00b0)<\/strong>.<br>\ud83d\udccf One leg is <strong>perpendicular<\/strong> to the bases.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-8486590d05d96f6f70beda01d5c76434\" style=\"color:#000060\">\ud83d\udfe5 <strong>\ud83d\udd39 Area and Perimeter Formulas<\/strong><\/h2>\n\n\n\n<p>\ud83d\udcd0 <strong>Area (A)<\/strong> = \u00bd \u00d7 (Sum of Parallel Sides) \u00d7 (Height)<br>\ud83d\udc49 A = \u00bd \u00d7 (a + b) \u00d7 h<\/p>\n\n\n\n<p>\ud83d\udccf <strong>Perimeter (P)<\/strong> = Sum of all four sides<br>\ud83d\udc49 P = a + b + c + d<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-ae3ea15ed9b37e44cacdfb93ce2c5a47\" style=\"color:#000060\">\ud83d\udfea <strong>\ud83d\udd39 Special Facts<\/strong><\/h2>\n\n\n\n<p>\ud83d\udca0 A <strong>parallelogram<\/strong> is <em>not<\/em> a trapezium because both pairs of sides are parallel.<br>\ud83d\udca0 A <strong>square or rectangle<\/strong> cannot be a trapezium.<br>\ud83d\udca0 Trapeziums are common in <strong>bridges, tables, and architectural designs<\/strong> \ud83c\udfd7\ufe0f.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-039e2f228201930b52cec3553fa5a838\" style=\"color:#000060\">\ud83c\udf1f <strong>\ud83d\udd39 Fun Tip<\/strong><\/h2>\n\n\n\n<p>Think of a trapezium as a <strong>\u201chalfway shape\u201d<\/strong> between a <strong>triangle<\/strong> and a <strong>parallelogram<\/strong>! \u23f9\ufe0f\u27a1\ufe0f\ud83d\udd3a<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#00056d\"><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:#f7faca\"><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>If UX is not parallel to VW , what is VW?<\/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.-1.png\" alt=\"\" class=\"wp-image-8616\" style=\"width:294px;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.-1.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.-1-300x300.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.-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>VW= ____<\/p>\n<\/div><\/div>\n\n\n\n<p>UVWX is a quadrilateral with exactly one pair of parallel sides, UV and WX , and one pair of congruent base angles, \u2220U and \u2220V.<\/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\/2024\/01\/image-removebg-preview-5.png\" alt=\"\" class=\"wp-image-11823\" style=\"width:296px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-5.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-5-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-5-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>So, UVWX is an isosceles trapezium.<\/p>\n\n\n\n<p>This means the legs are congruent. So, VW=UX=97.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b6fcd3\"><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>If CD is not parallel to AB , what is CD?<\/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.-1-1.png\" alt=\"\" class=\"wp-image-8621\" style=\"width:294px;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.-1-1.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.-1-1-300x300.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.-1-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>CD =_____ <\/p>\n<\/div><\/div>\n\n\n\n<p>ABCD is a quadrilateral with exactly one pair of parallel sides, AD and BC , and one pair of congruent base angles, \u2220D and \u2220A.<\/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_____4_9____9_4____4____9__and_____9____4_.__1_-removebg-preview-3.png\" alt=\"\" class=\"wp-image-8622\" style=\"width:292px;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_.__1_-removebg-preview-3.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_.__1_-removebg-preview-3-300x300.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_.__1_-removebg-preview-3-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>So, ABCD is an isosceles trapezium.<\/p>\n\n\n\n<p>This means the legs are congruent. So, CD=AB=19.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#e3daff\"><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\">If BE is not parallel to CD , what is BE?<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-17.png\" alt=\"\" class=\"wp-image-8625\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-17.png 670w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-17-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p>BE = ____<\/p>\n<\/div><\/div>\n\n\n\n<p>BCDE is a quadrilateral with exactly one pair of parallel sides, BC and DE , and one pair of congruent base angles, \u2220E and \u2220D.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design-removebg-preview-7.png\" alt=\"\" class=\"wp-image-8626\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design-removebg-preview-7.png 670w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design-removebg-preview-7-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p>So, BCDE is an isosceles trapezium.<\/p>\n\n\n\n<p>This means the legs are congruent. So, BE=CD=100.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s practice!<\/strong><\/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\/85123\/742\/328\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-46.png\" alt=\"\" class=\"wp-image-7815\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-46.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-46-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-46-150x150.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\/85329\/346\/611\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-55.png\" alt=\"\" class=\"wp-image-7816\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-55.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-55-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-55-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Properties of trapeziums Design by Delta publications key notes : \ud83d\udfe6 \ud83d\udd39 What is a Trapezium? A trapezium (also called a trapezoid) is a quadrilateral with one pair of parallel sides.\ud83d\udc49 The parallel sides are called bases, and the non-parallel sides are called legs. \ud83d\udfe9 \ud83d\udd39 Basic Properties of a Trapezium 1\ufe0f\u20e3 One Pair of<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/h-7-properties-of-trapeziums\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.7 Properties of trapeziums&#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-138","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/138","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=138"}],"version-history":[{"count":30,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/138\/revisions"}],"predecessor-version":[{"id":18178,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/138\/revisions\/18178"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}