{"id":313,"date":"2022-04-13T10:39:01","date_gmt":"2022-04-13T10:39:01","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=313"},"modified":"2025-03-03T10:23:39","modified_gmt":"2025-03-03T10:23:39","slug":"p-7-similarity-rules-for-triangles","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/p-7-similarity-rules-for-triangles\/","title":{"rendered":"P.7 Similarity rules for triangles"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Similarity rules for 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<p class=\"has-large-font-size\">Two&nbsp;triangles are similar if and only if they are scaled versions of each other. The ratios of their corresponding side lengths are equal and the measures of their corresponding angles are&nbsp;equal.<\/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-large-font-size\" style=\"background-color:#f3c8c8\"><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 has-link-color wp-elements-1536a074094e54064af504715c8e0a5f\" style=\"color:#b00012\"><strong>Are&nbsp;these triangles&nbsp;similar?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"919\" height=\"296\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-24.png\" alt=\"\" class=\"wp-image-11550\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-24.png 919w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-24-300x97.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-24-768x247.png 768w\" sizes=\"auto, (max-width: 919px) 100vw, 919px\" \/><\/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>Look&nbsp;at the&nbsp;diagram.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"881\" height=\"283\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-02T143230.218.png\" alt=\"\" class=\"wp-image-11553\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-02T143230.218.png 881w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-02T143230.218-300x96.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-02T143230.218-768x247.png 768w\" sizes=\"auto, (max-width: 881px) 100vw, 881px\" \/><\/figure><\/div>\n\n\n<p>Since&nbsp;\u2220T=\u2220I=54\u00b0and&nbsp;\u2220R=\u2220H=34\u00b0,\u2220T \u2245 \u2220I and&nbsp; \u2220R \u2245 \u2220H.<\/p>\n\n\n\n<p>Therefore,&nbsp;by the AA Similarity Theorem the triangles are&nbsp;similar.<\/p>\n\n\n\n<p>To&nbsp;write the similarity statement, match corresponding vertices:&nbsp;<\/p>\n\n\n\n<p>\u25b3RST ~ \u25b3HGI.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#edcee9\"><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 has-link-color wp-elements-1536a074094e54064af504715c8e0a5f\" style=\"color:#b00012\"><strong>Are&nbsp;these triangles&nbsp;similar?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"764\" height=\"418\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-25.png\" alt=\"\" class=\"wp-image-11557\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-25.png 764w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-25-300x164.png 300w\" sizes=\"auto, (max-width: 764px) 100vw, 764px\" \/><\/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>Since&nbsp;all three side lengths of&nbsp;\u25b3HIJ and&nbsp;\u25b3EFG are given, see if these triangles are similar by the SSS Similarity&nbsp;Theorem.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"675\" height=\"369\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-02T143751.533.png\" alt=\"\" class=\"wp-image-11558\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-02T143751.533.png 675w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-02T143751.533-300x164.png 300w\" sizes=\"auto, (max-width: 675px) 100vw, 675px\" \/><\/figure><\/div>\n\n\n<p>Remember&nbsp;that two triangles are similar if and only if they are scaled versions of each other. So, the shortest, middle, and longest sides in similar triangles are always corresponding. Therefore, if the ratios of the shortest, middle, and longest side lengths are not equal, the triangles are not&nbsp;similar.<\/p>\n\n\n\n<p>Pair&nbsp;the sides in order from shortest to longest:&nbsp; HI and EG , HJ and FG, and&nbsp;IJ and&nbsp; EF .<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"677\" height=\"369\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-02T144134.297.png\" alt=\"\" class=\"wp-image-11559\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-02T144134.297.png 677w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-02T144134.297-300x164.png 300w\" sizes=\"auto, (max-width: 677px) 100vw, 677px\" \/><\/figure><\/div>\n\n\n<p>Calculate&nbsp;the ratios of these three pairs of side&nbsp;lengths.<\/p>\n\n\n\n<p>HI \/ EG = 36 \/ 33 = 12 \/ 11<\/p>\n\n\n\n<p>HJ \/ FG = 40 \/ 45 = 8 \/ 9<\/p>\n\n\n\n<p>IJ \/ EF = 44 \/ 52 = 11 \/ 13<\/p>\n\n\n\n<p>Since&nbsp;HI \/ EG \u2260 HJ \/ FG , not all three pairs of sides are proportional. Therefore, the triangles are not&nbsp;similar.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#d6f4d2\"><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 has-link-color wp-elements-1536a074094e54064af504715c8e0a5f\" style=\"color:#b00012\"><strong>Are&nbsp;these triangles&nbsp;similar?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"614\" height=\"463\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-26.png\" alt=\"\" class=\"wp-image-11560\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-26.png 614w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-26-300x226.png 300w\" sizes=\"auto, (max-width: 614px) 100vw, 614px\" \/><\/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>Look&nbsp;at the&nbsp;diagram.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"575\" height=\"434\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-02T144756.725.png\" alt=\"\" class=\"wp-image-11561\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-02T144756.725.png 575w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-02T144756.725-300x226.png 300w\" sizes=\"auto, (max-width: 575px) 100vw, 575px\" \/><\/figure><\/div>\n\n\n<p>\u2220H \u2245 \u2220Q  and&nbsp;\u2220I \u2245 \u2220S.<\/p>\n\n\n\n<p>Therefore,&nbsp;by the AA Similarity Theorem the triangles are&nbsp;similar.<\/p>\n\n\n\n<p>To&nbsp;write the similarity statement, match corresponding vertices:&nbsp;<\/p>\n\n\n\n<p>\u25b3HIJ ~ \u25b3QSR.<\/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\/87775\/882\/461\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-105.png\" alt=\"\" class=\"wp-image-7191\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-105.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-105-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-105-150x150.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\/80839\/616\/322\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-123.png\" alt=\"\" class=\"wp-image-7193\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-123.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-123-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-123-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Similarity rules for triangles Key Notes : Two&nbsp;triangles are similar if and only if they are scaled versions of each other. The ratios of their corresponding side lengths are equal and the measures of their corresponding angles are&nbsp;equal. Learn with an example Are&nbsp;these triangles&nbsp;similar? Look&nbsp;at the&nbsp;diagram. Since&nbsp;\u2220T=\u2220I=54\u00b0and&nbsp;\u2220R=\u2220H=34\u00b0,\u2220T \u2245 \u2220I and&nbsp; \u2220R \u2245 \u2220H. Therefore,&nbsp;by the<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/p-7-similarity-rules-for-triangles\/\">Continue reading <span class=\"screen-reader-text\">&#8220;P.7 Similarity rules for 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-313","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/313","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=313"}],"version-history":[{"count":11,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/313\/revisions"}],"predecessor-version":[{"id":17559,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/313\/revisions\/17559"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=313"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}