{"id":118,"date":"2022-04-13T08:23:36","date_gmt":"2022-04-13T08:23:36","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=118"},"modified":"2025-10-24T06:10:39","modified_gmt":"2025-10-24T06:10:39","slug":"g-9-sss-theorem-in-the-coordinate-plane","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/g-9-sss-theorem-in-the-coordinate-plane\/","title":{"rendered":"G.9 SSS Theorem in the coordinate plane"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>SSS Theorem in the coordinate plane<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b;text-transform:capitalize\">key notes :<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-2d8c5be58a46262f80aa0fd8ee453964\" style=\"color:#000060\">\ud83d\udcd8 <strong>\ud83d\udd3a SSS Theorem (Side\u2013Side\u2013Side Theorem)<\/strong><\/h3>\n\n\n\n<p>\ud83d\udca1 The <strong>SSS Theorem<\/strong> states that:<\/p>\n\n\n\n<p>\u27a1\ufe0f <em>If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.<\/em> \ud83c\udfaf<\/p>\n\n\n\n<p><strong>Symbolically:<\/strong><\/p>\n\n\n\n<p>If <strong>AB = DE<\/strong>, <strong>BC = EF<\/strong>, and <strong>CA = FD<\/strong>,<br>then <strong>\u25b3ABC \u2245 \u25b3DEF<\/strong>. \u2705<\/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-a8829c8fad275f5f78017160d5063ff9\" style=\"color:#000060\">\ud83d\udccf <strong>In the Coordinate Plane \ud83e\uddee<\/strong><\/h3>\n\n\n\n<p>To apply the SSS Theorem in the coordinate plane:<br>We use the <strong>distance formula<\/strong> to find the lengths of the sides of triangles.<\/p>\n\n\n\n<p>\ud83e\udde0 <strong>Distance Formula:<\/strong> <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"288\" height=\"64\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/10\/image.png\" alt=\"\" class=\"wp-image-17976\" style=\"width:270px;height:auto\"\/><\/figure><\/div>\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-1c1fe2c0b5b402a17834e959b4720630\" style=\"color:#000060\">\ud83d\udd39 <strong>Steps to Prove SSS Theorem in the Coordinate Plane<\/strong><\/h3>\n\n\n\n<p>1\ufe0f\u20e3 <strong>Plot the Points<\/strong> on the coordinate plane. \ud83d\udcca<br>2\ufe0f\u20e3 <strong>Label the Triangles<\/strong> (e.g., \u25b3ABC and \u25b3DEF). \u270f\ufe0f<br>3\ufe0f\u20e3 <strong>Find the Lengths<\/strong> of all three sides using the <strong>distance formula<\/strong>. \ud83d\udcd0<br>4\ufe0f\u20e3 <strong>Compare the Sides:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If <strong>AB = DE<\/strong>, <strong>BC = EF<\/strong>, and <strong>CA = FD<\/strong>,<br>then triangles are <strong>congruent<\/strong> by <strong>SSS Theorem<\/strong>! \ud83c\udf89<\/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-450e00a5aea1938f329c41859e11bc28\" style=\"color:#000060\">\ud83e\udde9 <strong>Example<\/strong><\/h3>\n\n\n\n<p>Let\u2019s take two triangles:<br>A(1, 2), B(4, 6), C(5, 2)<br>and<br>D(2, 1), E(5, 5), F(6, 1)<\/p>\n\n\n\n<p>\ud83d\udc49 Use the distance formula to find all sides.<br>If all three pairs of sides are equal \u2014 \u2705<br>then <strong>\u25b3ABC \u2245 \u25b3DEF<\/strong> by <strong>SSS Theorem<\/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-text-color has-link-color has-large-font-size wp-elements-f97fa68ee512dd5797bbe709281aec07\" style=\"color:#000060\">\ud83c\udfc6 <strong>Why It\u2019s Important<\/strong><\/h3>\n\n\n\n<p>\u2728 Helps us prove triangles are congruent on the coordinate plane.<br>\u2728 Used in geometry, computer graphics, and architecture.<br>\u2728 Builds the base for proving other geometric properties.<\/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-5cc79842bc53f089a502384914ff80fb\" style=\"color:#000060\">\ud83c\udfa8 <strong>Quick Recap<\/strong><\/h3>\n\n\n\n<p>\ud83d\udd39 SSS = Side\u2013Side\u2013Side<br>\ud83d\udd39 Use the <strong>distance formula<\/strong> to check sides<br>\ud83d\udd39 Equal sides \u2192 Congruent triangles<br>\ud83d\udd39 Congruent triangles \u2192 Equal corresponding angles<\/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-2f1147473862232afaddb7c0623edc8a\" style=\"color:#000060\">\ud83d\udcac <strong>Memory Tip<\/strong><\/h3>\n\n\n\n<p>\ud83e\udde1 \u201c<strong>Three sides the same \u2013 triangles claim the same name!<\/strong>\u201d \ud83d\udd3a<\/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-normal-font-size\" style=\"background-color:#f4c0c0\"><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\">Are \u25b3ABC and \u25b3XYZ congruent?<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"582\" height=\"577\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image.png\" alt=\"\" class=\"wp-image-16557\" style=\"width:373px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image.png 582w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-300x297.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-150x150.png 150w\" sizes=\"auto, (max-width: 582px) 100vw, 582px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>yes<\/li>\n\n\n\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>To see that \u25b3ABC and \u25b3XYZ are not congruent, calculate the three side lengths of each triangle.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"580\" height=\"582\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-2.png\" alt=\"\" class=\"wp-image-16559\" style=\"width:371px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-2.png 580w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-2-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-2-150x150.png 150w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-2-400x400.png 400w\" sizes=\"auto, (max-width: 580px) 100vw, 580px\" \/><\/figure><\/div>\n\n\n<p>\u25b3ABC has vertices A(9,\u20132), B(9,9) and C(0,9) and \u25b3XYZ has vertices X(2,\u20131), Y(\u20139,\u20131) and Z(\u20139,\u20139).<\/p>\n\n\n\n<p><strong>Step 1: Find the side lengths of \u25b3ABC.<\/strong><\/p>\n\n\n\n<p>First, find AB. Since A(9,\u20132) and B(9,9) have the same x-coordinate, AB is the absolute value of the difference in the y-coordinates. So, AB=|9\u2013 \u20132|=11.<\/p>\n\n\n\n<p>Second, find BC. Since B(9,9) and C(0,9) have the same y-coordinate, BC is the absolute value of the difference in the x-coordinates. So, BC=|0\u20139|=9.<\/p>\n\n\n\n<p>Third, find AC. Since A(9,\u20132) and C(0,9) do not have equal x-coordinates or equal y-coordinates, use the distance formula to calculate AC. Plug in A(9,\u20132) for (x<sub>1<\/sub>,y<sub>1<\/sub>) and C(0,9) for (x<sub>2<\/sub>,y<sub>2<\/sub>), and simplify.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"779\" height=\"320\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-removebg-preview-65.png\" alt=\"\" class=\"wp-image-16561\" style=\"width:575px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-removebg-preview-65.png 779w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-removebg-preview-65-300x123.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-removebg-preview-65-768x315.png 768w\" sizes=\"auto, (max-width: 779px) 100vw, 779px\" \/><\/figure><\/div>\n\n\n<p>The three side lengths of \u25b3ABC are AB=11, BC=9, and AC=202.<\/p>\n\n\n\n<p><strong>Step 2: Find the side lengths of \u25b3XYZ.<\/strong><\/p>\n\n\n\n<p>First, find XY. Since X(2,\u20131) and Y(\u20139 , \u20131) have the same y-coordinate, XY is the absolute value of the difference in the x-coordinates. So, XY = |\u2013 9 \u20132| = 11.<\/p>\n\n\n\n<p>Second, find YZ. Since Y(\u20139,\u20131) and Z(\u20139,\u20139) have the same x-coordinate, YZ is the absolute value of the difference in the y-coordinates. So, YZ = | \u20139\u2013 \u20131| = 8.<\/p>\n\n\n\n<p>Since no side of \u25b3ABC has length 8, YZ is not congruent to AB , BC, or AC. Therefore, \u25b3ABC is not congruent to \u25b3XYZ by the SSS Theorem.<\/p>\n<\/div><\/div>\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<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#d7ebce\"><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\">Are \u25b3GHI and \u25b3WXY congruent?<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"585\" height=\"581\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-4.png\" alt=\"\" class=\"wp-image-16563\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-4.png 585w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-4-300x298.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-4-150x150.png 150w\" sizes=\"auto, (max-width: 585px) 100vw, 585px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>yes<\/li>\n\n\n\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>To see that \u25b3GHI and \u25b3WXY are not congruent, calculate the three side lengths of each triangle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"595\" height=\"581\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-5.png\" alt=\"\" class=\"wp-image-16565\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-5.png 595w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-5-300x293.png 300w\" sizes=\"auto, (max-width: 595px) 100vw, 595px\" \/><\/figure>\n\n\n\n<p>\u25b3GHI has vertices G(0,\u20137), H(\u20139,3) and I(\u20139,\u20137) and \u25b3WXY has vertices W(7,9), X(\u20133,1) and Y(7,1).<\/p>\n\n\n\n<p><strong>Step 1: Find the side lengths of \u25b3GHI.<\/strong><\/p>\n\n\n\n<p>First, find GI. Since G(0,\u20137) and I(\u20139,\u20137) have the same y-coordinate, GI is the absolute value of the difference in the x-coordinates. So, GI=|\u20139\u20130|=9.<\/p>\n\n\n\n<p>Second, find HI. Since H(\u20139,3) and I(\u20139,\u20137) have the same x-coordinate, HI is the absolute value of the difference in the y-coordinates. So, HI=|\u20137\u20133|=10.<\/p>\n\n\n\n<p>Third, find GH. Since G(0,\u20137) and H(\u20139,3) do not have equal x-coordinates or equal y-coordinates, use the distance formula to calculate GH. Plug in G(0,\u20137) for (x<sub>1<\/sub>,y<sub>1<\/sub>) and H(\u20139,3) for (x<sub>2<\/sub>,y<sub>2<\/sub>), and simplify.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"767\" height=\"325\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-removebg-preview-66.png\" alt=\"\" class=\"wp-image-16567\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-removebg-preview-66.png 767w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2025\/02\/image-removebg-preview-66-300x127.png 300w\" sizes=\"auto, (max-width: 767px) 100vw, 767px\" \/><\/figure>\n\n\n\n<p>The three side lengths of \u25b3GHI are GI=9, HI=10, and GH=181.<\/p>\n\n\n\n<p><strong>Step 2: Find the side lengths of \u25b3WXY.<\/strong><\/p>\n\n\n\n<p>First, find XY. Since X(\u20133,1) and Y(7,1) have the same y-coordinate, XY is the absolute value of the difference in the x-coordinates. So, XY=|7\u2013 \u20133|=10.<\/p>\n\n\n\n<p>Second, find WY. Since W(7,9) and Y(7,1) have the same x-coordinate, WY is the absolute value of the difference in the y-coordinates. So, WY=|1\u20139|=8.<\/p>\n\n\n\n<p>Since no side of \u25b3GHI has length 8, WY is not congruent to GI , HI, or GH. Therefore, \u25b3GHI is not congruent to \u25b3WXY by the SSS Theorem.<\/p>\n<\/div><\/div>\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\/81355\/407\/542\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-34.png\" alt=\"\" class=\"wp-image-7757\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-34.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-34-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-34-150x150.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\/671\/265\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-37.png\" alt=\"\" class=\"wp-image-7758\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-37.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-37-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-37-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>SSS Theorem in the coordinate plane key notes : \ud83d\udcd8 \ud83d\udd3a SSS Theorem (Side\u2013Side\u2013Side Theorem) \ud83d\udca1 The SSS Theorem states that: \u27a1\ufe0f If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent. \ud83c\udfaf Symbolically: If AB = DE, BC = EF, and CA<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/g-9-sss-theorem-in-the-coordinate-plane\/\">Continue reading <span class=\"screen-reader-text\">&#8220;G.9 SSS Theorem in the coordinate plane&#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-118","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/118","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=118"}],"version-history":[{"count":41,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/118\/revisions"}],"predecessor-version":[{"id":18127,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/118\/revisions\/18127"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}