{"id":232,"date":"2022-04-13T10:24:23","date_gmt":"2022-04-13T10:24:23","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=232"},"modified":"2025-01-31T11:37:19","modified_gmt":"2025-01-31T11:37:19","slug":"l-5-congruent-line-segments","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/l-5-congruent-line-segments\/","title":{"rendered":"L.5 Congruent line segments"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Congruent line segments<\/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<p class=\"has-large-font-size\">Two&nbsp;segments are&nbsp;<strong>congruent<\/strong>&nbsp;(\u2245)&nbsp;if they have the same&nbsp;length.<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">Introduction:<\/h2>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Definition of Congruence:<\/strong> In geometry, the term &#8220;congruence&#8221; indicates that two geometric figures are identical in shape and size. When it comes to line segments, congruence implies that two segments have the same length.<\/li>\n\n\n\n<li><strong>Congruent Line Segments:<\/strong> Line segments are congruent if they have equal lengths. This concept is fundamental in geometry and plays a crucial role in various geometric proofs and constructions.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">Properties of Congruent Line Segments:<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Equal Lengths:<\/strong>\n<ul class=\"wp-block-list\">\n<li>The most fundamental property of congruent line segments is that they have the same length.<\/li>\n\n\n\n<li>If <em>A<\/em><em>B<\/em> and <em>C<\/em><em>D<\/em> are congruent line segments, then the measure of <em>A<\/em><em>B<\/em> is equal to the measure of <em>C<\/em><em>D<\/em>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li class=\"has-large-font-size\"><strong>Symbolic Representation:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Congruent line segments are often denoted using the symbol \u2245.<\/li>\n\n\n\n<li>For example, if <em>A<\/em><em>B<\/em>\u2245<em>C<\/em><em>D<\/em>, it signifies that line segments <em>A<\/em><em>B<\/em> and <em>C<\/em><em>D<\/em> are congruent.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">Methods of Proving Congruent Line Segments:<\/h2>\n\n\n\n<ol class=\"wp-block-list has-large-font-size\">\n<li><strong>Measurement:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Direct measurement using a ruler is the simplest way to show that two line segments are congruent.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Congruence Postulates:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Side-Side-Side (SSS) Congruence Postulate: If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.<\/li>\n\n\n\n<li>Side-Angle-Side (SAS) Congruence Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\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:#e7d2f0\"><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 class=\"has-text-color has-link-color wp-elements-479cf396ed1c8fb03ed57220978cf0ea\" style=\"color:#b00012\"><strong>Are&nbsp;WX&nbsp;and&nbsp;UY&nbsp;congruent?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"405\" height=\"349\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/image-30.png\" alt=\"\" class=\"wp-image-10010\" style=\"width:324px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/image-30.png 405w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/image-30-300x259.png 300w\" sizes=\"auto, (max-width: 405px) 100vw, 405px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>yes<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Look&nbsp;at the diagram and compare WX to UY .<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__19_-removebg-preview.png\" alt=\"\" class=\"wp-image-10949\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__19_-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__19_-removebg-preview-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__19_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>WX is 82 Centimeters  long and UY is 82 Centimeters long . WX and UY have the same length , so WX and UY are congruent . <\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f8a1ab\"><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 class=\"has-text-color has-link-color wp-elements-295d439dca7ee563e75c1610f8b85510\" style=\"color:#b00012\"><strong>Are&nbsp;EF&nbsp;and&nbsp;FG&nbsp;congruent?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"336\" height=\"314\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/image-32.png\" alt=\"\" class=\"wp-image-10012\" style=\"width:343px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/image-32.png 336w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/image-32-300x280.png 300w\" sizes=\"auto, (max-width: 336px) 100vw, 336px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>yes<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Look&nbsp;at the diagram and compare EF to FG .<\/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__20_-removebg-preview.png\" alt=\"\" class=\"wp-image-10953\" style=\"width:462px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__20_-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__20_-removebg-preview-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__20_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>EF is 165 millimeters long and FG is 165 millimeters long . EF and FG have the same same length , so EF and FG are congruent<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#d9d6ed\"><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 class=\"has-text-color has-link-color wp-elements-3caa415e97bf7f5a21e166c9e05a7588\" style=\"color:#b00012\"><strong> Are&nbsp;IJ&nbsp;and&nbsp;GH&nbsp;congruent?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"456\" height=\"329\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/image-34.png\" alt=\"\" class=\"wp-image-10014\" style=\"width:421px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/image-34.png 456w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/image-34-300x216.png 300w\" sizes=\"auto, (max-width: 456px) 100vw, 456px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>yes<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Look&nbsp;at the diagram and compare IJ to GH .<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__21_-removebg-preview.png\" alt=\"\" class=\"wp-image-10957\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__21_-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__21_-removebg-preview-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled_design__21_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>IJ = 131 and GH = 166 . IJ  \u2260 GH , so IJ and GH are not congruent .<font color=\"#202124\" face=\"Google Sans, arial, sans-serif\"><span style=\"font-size: 32px; white-space-collapse: collapse; background-color: rgb(255, 255, 255);\"><\/span><\/font><\/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\/85891\/570\/762\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-69.png\" alt=\"\" class=\"wp-image-7037\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-69.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-69-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-69-150x150.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\/37927\/121\/136\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-87.png\" alt=\"\" class=\"wp-image-7038\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-87.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-87-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-87-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Congruent line segments Key Notes : Two&nbsp;segments are&nbsp;congruent&nbsp;(\u2245)&nbsp;if they have the same&nbsp;length. Introduction: Properties of Congruent Line Segments: Methods of Proving Congruent Line Segments: Learn with an example Are&nbsp;WX&nbsp;and&nbsp;UY&nbsp;congruent? Look&nbsp;at the diagram and compare WX to UY . WX is 82 Centimeters long and UY is 82 Centimeters long . WX and UY have the<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/l-5-congruent-line-segments\/\">Continue reading <span class=\"screen-reader-text\">&#8220;L.5 Congruent line segments&#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-232","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/232","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=232"}],"version-history":[{"count":18,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/232\/revisions"}],"predecessor-version":[{"id":17493,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/232\/revisions\/17493"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=232"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}