{"id":114,"date":"2022-04-13T08:22:45","date_gmt":"2022-04-13T08:22:45","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=114"},"modified":"2025-10-31T09:16:39","modified_gmt":"2025-10-31T09:16:39","slug":"g-7-midsegments-of-triangles","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/g-7-midsegments-of-triangles\/","title":{"rendered":"G.7 Midsegments of triangles"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Midsegments of triangles<\/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\/DAG3Wf1VPn0\/v0qhkTZJ0TmZktca7SHfUg\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3Wf1VPn0&#x2F;v0qhkTZJ0TmZktca7SHfUg&#x2F;watch?utm_content=DAG3Wf1VPn0&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-4f178d8a0ac06a280f2be87b562f440f\" style=\"color:#0e6745\">\ud83c\udf1f <strong>Midsegments of Triangles<\/strong> \ud83c\udf1f<\/h2>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-fa6b2ff389d394d168f3be59ca8a65e8\" style=\"color:#000060\"><strong>Definition<\/strong><\/h3>\n\n\n\n<p>A <strong>midsegment<\/strong> of a triangle is a line segment that <strong>connects the midpoints of two sides<\/strong> of a triangle.<br>\u270f\ufe0f <em>Think of it as the &#8220;middle connector&#8221;!<\/em><\/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-fce0ceec46b1400006f13bb166a41f63\" style=\"color:#000060\"><strong>Key Properties<\/strong> \u2705<\/h3>\n\n\n\n<p><strong>Parallel to the third side<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The midsegment is always <strong>parallel<\/strong> to the side of the triangle that it does <strong>not touch<\/strong>.<\/li>\n\n\n\n<li>\ud83d\udfe2 Example: If AB and AC are sides, and D and E are their midpoints, then <strong>DE \u2225 BC<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p><strong>Half the length of the third side<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The length of the midsegment = <strong>\u00bd \u00d7 length of the side it is parallel to<\/strong>.<\/li>\n\n\n\n<li>\u2728 Formula: <strong>DE = \u00bd \u00d7 BC<\/strong><\/li>\n<\/ul>\n\n\n\n<p><strong>Forms a smaller triangle inside<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Two midsegments can form a <strong>triangle inside the original triangle<\/strong>, similar to the main triangle.<\/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-655a031ceb841a0ae0da2bad2fe9cca1\" style=\"color:#000060\"><strong>How to Identify a Midsegment<\/strong> \ud83d\udd0d<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Look for points <strong>exactly halfway<\/strong> along two sides.<\/li>\n\n\n\n<li>Connect them with a <strong>straight line<\/strong>.<\/li>\n\n\n\n<li>Check if it is <strong>parallel<\/strong> to the third side and <strong>half its length<\/strong>.<\/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-f7fd78d3b00ca6f2b0efd78b07de9c60\" style=\"color:#000060\"><strong>Uses of Midsegments<\/strong> \ud83d\udee0\ufe0f<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Helps in <strong>finding missing lengths<\/strong> in triangles.<\/li>\n\n\n\n<li>Used in <strong>coordinate geometry<\/strong> to find midpoints and slope relationships.<\/li>\n\n\n\n<li>Makes <strong>triangles similar<\/strong> and <strong>proves congruence<\/strong> in parts of triangles.<\/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-936c2278f60adb01a5c89ff3305e2c69\" style=\"color:#000060\"><strong>Fun Visual Tip<\/strong> \ud83c\udfa8<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw a triangle \ud83d\udec6<\/li>\n\n\n\n<li>Mark midpoints of two sides \ud83d\udd39<\/li>\n\n\n\n<li>Connect them \ud83d\udd38<\/li>\n\n\n\n<li>Notice how the midsegment forms a <strong>mini parallel line<\/strong> inside the triangle<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-7e727fa9bbb7b8870ac755d9ee669b0c\" style=\"color:#000060\">\u2705 <strong>Remember:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Midsegment = <strong>connects midpoints<\/strong><\/li>\n\n\n\n<li>Parallel to third side \u2225<\/li>\n\n\n\n<li>Length = <strong>\u00bd of third side<\/strong><\/li>\n<\/ul>\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-primary-color has-text-color has-background has-link-color has-normal-font-size wp-elements-4f3cde20c6f29435f47e28c82e7ac561\" style=\"background-color:#c7faee\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-bf5a3f50a0f646f554a1da830e48f0f1\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>SU&nbsp;is a midsegment of&nbsp;\u25b3TVW.<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>If&nbsp;<em>VW<\/em> = 44,&nbsp;what is&nbsp;<em>SU<\/em>?<\/strong><\/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\/2024\/01\/Untitled-design-15.png\" alt=\"\" class=\"wp-image-11745\" style=\"aspect-ratio:1;width:334px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/Untitled-design-15.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/Untitled-design-15-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/Untitled-design-15-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>SU =<\/p>\n<\/div><\/div>\n\n\n\n<p>SU&nbsp;is a midsegment of&nbsp;\u25b3TVW.<\/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\/2022\/10\/Untitled_design__62_-removebg-preview.png\" alt=\"\" class=\"wp-image-3053\" style=\"aspect-ratio:1;width:344px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/10\/Untitled_design__62_-removebg-preview.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/10\/Untitled_design__62_-removebg-preview-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/10\/Untitled_design__62_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>So,&nbsp;<em>SU<\/em>&nbsp;is half of&nbsp;<em>VW<\/em>.&nbsp;Set&nbsp;<em>SU<\/em>&nbsp;equal to half of&nbsp;<em>VW<\/em>&nbsp;and solve for&nbsp;<em>SU<\/em>.<\/p>\n\n\n\n<p><em>SU<\/em> = VW\/2<\/p>\n\n\n\n<p>= 44\/2 &#8212;&gt; <em>Plug&nbsp;in&nbsp;<\/em>VW=44<\/p>\n\n\n\n<p>= 22 &#8212;&gt; <em>Divide<\/em><\/p>\n\n\n\n<p>So,&nbsp;<em>SU<\/em> = 22.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-normal-font-size wp-elements-ee4c890af7291119d951076445c12c0d\" style=\"background-color:#f0d6ff\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-f587fb457b737132dd23d90c7d3c8ee0\"><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 PR = 20, what is ST?<\/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\/Untitled_design__4_-removebg-preview-2.png\" alt=\"\" class=\"wp-image-8499\" style=\"width:324px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__4_-removebg-preview-2.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__4_-removebg-preview-2-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__4_-removebg-preview-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>ST = ____<\/p>\n<\/div><\/div>\n\n\n\n<p>Since&nbsp;P&nbsp;is the midpoint of&nbsp;QT and R is the midpoint of QS . PR is a midsegment of \u25b3QST.<\/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\/Untitled_design__4_-removebg-preview-3.png\" alt=\"\" class=\"wp-image-8500\" style=\"width:356px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__4_-removebg-preview-3.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__4_-removebg-preview-3-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__4_-removebg-preview-3-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>So, PR is half of ST. In other words, ST is twice PR. Set ST equal to twice PR and solve for ST.<\/p>\n\n\n\n<p>ST= 2 . PR<\/p>\n\n\n\n<p>= 2(20) Plug in PR = 20<\/p>\n\n\n\n<p>= 40         Multiply<\/p>\n\n\n\n<p>So, ST = 40.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-normal-font-size wp-elements-73d54eb490af71830d8619e8540dc8b9\" style=\"background-color:#d6d2fa\"><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 PR = 35, what is ST?<\/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\/Untitled-design-11.png\" alt=\"\" class=\"wp-image-8502\" style=\"width:388px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-11.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-11-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-11-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>ST =<\/p>\n<\/div><\/div>\n\n\n\n<p>Since PT \u2245 PQ and RS \u2245 QR , PR is a midsegment of \u25b3QST.<\/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\/Untitled_design-removebg-preview-3.png\" alt=\"\" class=\"wp-image-8504\" style=\"width:336px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design-removebg-preview-3.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design-removebg-preview-3-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design-removebg-preview-3-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>So,&nbsp;<em>PR<\/em>&nbsp;is half of&nbsp;<em>ST<\/em>.&nbsp;In other words,&nbsp;<em>ST<\/em>&nbsp;is twice&nbsp;<em>PR<\/em>.&nbsp;Set&nbsp;<em>ST<\/em>&nbsp;equal to twice&nbsp;<em>PR<\/em>&nbsp;and solve for&nbsp;<em>ST<\/em>.<\/p>\n\n\n\n<p>ST = 2 . PR<\/p>\n\n\n\n<p>= 2(35) Plug in PR = 35<\/p>\n\n\n\n<p>= 70           Multiply<\/p>\n\n\n\n<p>So, ST=70.<\/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!\u270d\ufe0f<\/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\/81353\/009\/231\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-38.png\" alt=\"\" class=\"wp-image-7786\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-38.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-38-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-38-150x150.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\/81098\/149\/545\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-47.png\" alt=\"\" class=\"wp-image-7787\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-47.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-47-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-47-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Midsegments of triangles Design by Delta publications key notes : \ud83c\udf1f Midsegments of Triangles \ud83c\udf1f Definition A midsegment of a triangle is a line segment that connects the midpoints of two sides of a triangle.\u270f\ufe0f Think of it as the &#8220;middle connector&#8221;! Key Properties \u2705 Parallel to the third side Half the length of the<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/g-7-midsegments-of-triangles\/\">Continue reading <span class=\"screen-reader-text\">&#8220;G.7 Midsegments of triangles&#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-114","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/114","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=114"}],"version-history":[{"count":22,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/114\/revisions"}],"predecessor-version":[{"id":18161,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/114\/revisions\/18161"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}