{"id":289,"date":"2022-04-13T10:34:40","date_gmt":"2022-04-13T10:34:40","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=289"},"modified":"2024-10-23T14:25:20","modified_gmt":"2024-10-23T14:25:20","slug":"o-3-midsegments-of-triangles","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/o-3-midsegments-of-triangles\/","title":{"rendered":"O.3 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<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-8550df6181cd5d83aa7a08ef336a4ca1\" style=\"color:#74008b\">Key Notes :<\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<h4 class=\"wp-block-heading\">1. <strong>Definition of a Midsegment<\/strong>:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>midsegment<\/strong> of a triangle is a line segment that connects the midpoints of two sides of the triangle.<\/li>\n\n\n\n<li>Each triangle has <strong>three midsegments<\/strong>, one for each pair of sides.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">2. <strong>Properties of the Midsegment<\/strong>:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Parallelism<\/strong>: The midsegment is <strong>parallel<\/strong> to the third side of the triangle (the side not connected by the midsegment).<\/li>\n\n\n\n<li><strong>Length<\/strong>: The length of the midsegment is <strong>half the length<\/strong> of the third side.\n<ul class=\"wp-block-list\">\n<li>If the third side is denoted as ( AB ) and the midsegment connects the midpoints of ( AC ) and ( BC ), then ( \\text{Midsegment} = \\frac{1}{2} \\times AB ).<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Divides the Triangle<\/strong>: The midsegment divides the triangle into two smaller triangles, each of which is similar to the original triangle by the <strong>Side-Angle-Side (SAS) Similarity Theorem<\/strong>.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">3. <strong>Triangle Midsegment Theorem<\/strong>:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>This theorem states:\n<ul class=\"wp-block-list\">\n<li>A midsegment of a triangle is <strong>parallel<\/strong> to one side of the triangle and its length is <strong>half<\/strong> the length of that side.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>The theorem can be used to solve problems involving triangle side lengths and parallel lines.<\/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<br><\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f6e1e1\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>If&nbsp;<em>TV<\/em>=48, what  is &nbsp;<em>SW<\/em>?<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"438\" height=\"461\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-48.png\" alt=\"\" class=\"wp-image-11350\" style=\"width:356px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-48.png 438w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-48-285x300.png 285w\" sizes=\"auto, (max-width: 438px) 100vw, 438px\" \/><\/figure><\/div>\n\n\n<p>SW = ______<\/p>\n<\/div><\/div>\n\n\n\n<p>Since&nbsp;VW\u2245UV&nbsp;and&nbsp;ST\u2245TU,TV&nbsp;is a midsegment of&nbsp;\u25b3SUW.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"438\" height=\"461\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-30T132005.304.png\" alt=\"\" class=\"wp-image-11353\" style=\"width:495px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-30T132005.304.png 438w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-30T132005.304-285x300.png 285w\" sizes=\"auto, (max-width: 438px) 100vw, 438px\" \/><\/figure><\/div>\n\n\n<p>So,&nbsp;TV&nbsp;is half of&nbsp;SW.&nbsp;In other words,&nbsp;SW&nbsp;is twice&nbsp;TV.&nbsp;Set&nbsp;SW&nbsp;equal to twice&nbsp;TV&nbsp;and solve for&nbsp;SW.<\/p>\n\n\n\n<p><em>SW<\/em> = 2  . <em>TV<\/em><\/p>\n\n\n\n<p>      = 2(<strong>48<\/strong>)    Plug&nbsp;in&nbsp;TV=48<\/p>\n\n\n\n<p>      = 96     Multiply<\/p>\n\n\n\n<p>So,&nbsp;<em>SW<\/em>=96.<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b4eaa1\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>\ud83d\udcda If&nbsp;<em>WX<\/em>=66,&nbsp;what is&nbsp;<em>VY<\/em>?<\/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:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-39.png\" alt=\"\" class=\"wp-image-11354\" style=\"width:428px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-39.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-39-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-39-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>VY = ______<\/p>\n<\/div><\/div>\n\n\n\n<p>Since&nbsp;XY\u2245YZ&nbsp;and&nbsp;VW\u2245VZ, VY&nbsp;is a midsegment of&nbsp;\u25b3WXZ.<\/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:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-30T132339.284.png\" alt=\"\" class=\"wp-image-11355\" style=\"width:358px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-30T132339.284.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-30T132339.284-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-30T132339.284-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>So,&nbsp;VY&nbsp;is half of&nbsp;WX.&nbsp;Set&nbsp;VY&nbsp;equal to half of &nbsp;WX&nbsp;and solve for&nbsp;VY.<\/p>\n\n\n\n<p>VY = WX \/ 2<\/p>\n\n\n\n<p>      = 66\/2    Plug&nbsp;in&nbsp;WX=66<\/p>\n\n\n\n<p>      = 33     <em>Divide<\/em><\/p>\n\n\n\n<p>So,&nbsp;<em>VY<\/em>=33.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f4bdee\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p> \ud83d\udcda If&nbsp;<em>UV<\/em>=22,&nbsp;what is&nbsp;<em>WY<\/em>?<\/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:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-40.png\" alt=\"\" class=\"wp-image-11357\" style=\"width:366px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-40.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-40-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-40-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>WY =_________<\/p>\n<\/div><\/div>\n\n\n\n<p>Since&nbsp;VW \u2245 WX&nbsp;and&nbsp;UY \u2245 XY, WY&nbsp;is a midsegment of&nbsp;\u25b3UVX.<\/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:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-30T133034.747.png\" alt=\"\" class=\"wp-image-11358\" style=\"width:424px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-30T133034.747.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-30T133034.747-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-2023-12-30T133034.747-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>So,&nbsp;WY&nbsp;is half of&nbsp;UY.&nbsp;Set&nbsp;WY&nbsp;equal to half of &nbsp;UY&nbsp;and solve for&nbsp;WY.<\/p>\n\n\n\n<p>WY = UY \/ 2<\/p>\n\n\n\n<p>      = 22\/2    Plug&nbsp;in&nbsp;UV=22<\/p>\n\n\n\n<p>      = 11     <em>Divide<\/em><\/p>\n\n\n\n<p>So,&nbsp;WY=11.<\/p>\n<\/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\/80409\/703\/727\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-94.png\" alt=\"\" class=\"wp-image-7138\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-94.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-94-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-94-150x150.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\/80171\/009\/452\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-112.png\" alt=\"\" class=\"wp-image-7139\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-112.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-112-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-112-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Midsegments of triangles Key Notes : 1. Definition of a Midsegment: 2. Properties of the Midsegment: 3. Triangle Midsegment Theorem: Learn with an example If&nbsp;TV=48, what is &nbsp;SW? SW = ______ Since&nbsp;VW\u2245UV&nbsp;and&nbsp;ST\u2245TU,TV&nbsp;is a midsegment of&nbsp;\u25b3SUW. So,&nbsp;TV&nbsp;is half of&nbsp;SW.&nbsp;In other words,&nbsp;SW&nbsp;is twice&nbsp;TV.&nbsp;Set&nbsp;SW&nbsp;equal to twice&nbsp;TV&nbsp;and solve for&nbsp;SW. SW = 2 . TV = 2(48) Plug&nbsp;in&nbsp;TV=48 = 96<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/o-3-midsegments-of-triangles\/\">Continue reading <span class=\"screen-reader-text\">&#8220;O.3 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-289","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/289","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=289"}],"version-history":[{"count":12,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/289\/revisions"}],"predecessor-version":[{"id":14308,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/289\/revisions\/14308"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=289"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}