{"id":11338,"date":"2022-07-07T20:05:42","date_gmt":"2022-07-07T14:35:42","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11338"},"modified":"2022-07-07T20:05:47","modified_gmt":"2022-07-07T14:35:47","slug":"in-the-figure-qrover-qs-qtover-pr-and-angle-1-angle-2-show-that-triangle-pqs-triangle-tqr","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/in-the-figure-qrover-qs-qtover-pr-and-angle-1-angle-2-show-that-triangle-pqs-triangle-tqr\/","title":{"rendered":"In the figure, \\(QR\\over QS\\) = \\(QT\\over PR\\) and \\(\\angle\\) 1 = \\(\\angle\\) 2. Show that \\(\\triangle\\) PQS ~ \\(\\triangle\\) TQR."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>Given,\u00a0 <img decoding=\"async\" loading=\"lazy\" class=\" wp-image-11339 alignright\" src=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-3-4.jpeg?resize=211%2C142&#038;ssl=1\" alt=\"triangle\" width=\"211\" height=\"142\" srcset=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-3-4.jpeg?resize=300%2C201&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-3-4.jpeg?resize=1024%2C686&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-3-4.jpeg?resize=768%2C515&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-3-4.jpeg?resize=1536%2C1029&amp;ssl=1 1536w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-3-4.jpeg?w=1700&amp;ssl=1 1700w\" sizes=\"(max-width: 211px) 100vw, 211px\" data-recalc-dims=\"1\" \/>\\(QR\\over QS\\) = \\(QT\\over PR\\)<\/p>\n<p>So, \\(QT\\over QR\\) = \\(PR\\over QS\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;&#8230;.(1)<\/p>\n<p>Also given,\u00a0 \\(\\angle\\) 1 = \\(\\angle\\) 2<\/p>\n<p>Since, sides opposite to equal \\(\\angle\\)s are equal,<\/p>\n<p>So , PR = PQ\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 &#8230;&#8230;&#8230;(2)<\/p>\n<p>From (1) and (2), we get<\/p>\n<p>\\(QT\\over QR\\) = \\(PQ\\over QS\\)\u00a0 \u00a0 \u00a0 or\u00a0 \u00a0 \\(PQ\\over QT\\) = \\(QS\\over QR\\)<\/p>\n<p>In \\(\\triangle\\)s PQS and TQR, we have :<\/p>\n<p>\\(PQ\\over QT\\) = \\(QS\\over QR\\)\u00a0 \u00a0 \u00a0and\u00a0 \u00a0 \\(\\angle\\) PQS = \\(\\angle\\) TQR\u00a0 = \\(\\angle\\) Q<\/p>\n<p>Hence, By SAS criterion of similarity, <strong>\\(\\triangle\\) PQS ~ \\(\\triangle\\) TQR<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : Given,\u00a0 \\(QR\\over QS\\) = \\(QT\\over PR\\) So, \\(QT\\over QR\\) = \\(PR\\over QS\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;&#8230;.(1) Also given,\u00a0 \\(\\angle\\) 1 = \\(\\angle\\) 2 Since, sides opposite to equal \\(\\angle\\)s are equal, So , PR = PQ\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 &#8230;&#8230;&#8230;(2) From (1) and (2), we get \\(QT\\over &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/in-the-figure-qrover-qs-qtover-pr-and-angle-1-angle-2-show-that-triangle-pqs-triangle-tqr\/\"> <span class=\"screen-reader-text\">In the figure, \\(QR\\over QS\\) = \\(QT\\over PR\\) and \\(\\angle\\) 1 = \\(\\angle\\) 2. Show that \\(\\triangle\\) PQS ~ \\(\\triangle\\) TQR.<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,912],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>In the figure, \\(QR\\over QS\\) = \\(QT\\over PR\\) and \\(\\angle\\) 1 = \\(\\angle\\) 2. Show that \\(\\triangle\\) PQS ~ \\(\\triangle\\) TQR. - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/in-the-figure-qrover-qs-qtover-pr-and-angle-1-angle-2-show-that-triangle-pqs-triangle-tqr\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"In the figure, \\(QR\\over QS\\) = \\(QT\\over PR\\) and \\(\\angle\\) 1 = \\(\\angle\\) 2. Show that \\(\\triangle\\) PQS ~ \\(\\triangle\\) TQR. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Given,\u00a0 (QRover QS) = (QTover PR) So, (QTover QR) = (PRover QS)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;&#8230;.(1) Also given,\u00a0 (angle) 1 = (angle) 2 Since, sides opposite to equal (angle)s are equal, So , PR = PQ\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 &#8230;&#8230;&#8230;(2) From (1) and (2), we get (QTover &hellip; In the figure, (QRover QS) = (QTover PR) and (angle) 1 = (angle) 2. Show that (triangle) PQS ~ (triangle) TQR. Read More &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/in-the-figure-qrover-qs-qtover-pr-and-angle-1-angle-2-show-that-triangle-pqs-triangle-tqr\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2022-07-07T14:35:42+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-07-07T14:35:47+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-3-4-300x201.jpeg\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/in-the-figure-qrover-qs-qtover-pr-and-angle-1-angle-2-show-that-triangle-pqs-triangle-tqr\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/in-the-figure-qrover-qs-qtover-pr-and-angle-1-angle-2-show-that-triangle-pqs-triangle-tqr\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"In the figure, \\\\(QR\\\\over QS\\\\) = \\\\(QT\\\\over PR\\\\) and \\\\(\\\\angle\\\\) 1 = \\\\(\\\\angle\\\\) 2. 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Show that \\(\\triangle\\) PQS ~ \\(\\triangle\\) TQR. - Mathemerize","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/in-the-figure-qrover-qs-qtover-pr-and-angle-1-angle-2-show-that-triangle-pqs-triangle-tqr\/","og_locale":"en_US","og_type":"article","og_title":"In the figure, \\(QR\\over QS\\) = \\(QT\\over PR\\) and \\(\\angle\\) 1 = \\(\\angle\\) 2. Show that \\(\\triangle\\) PQS ~ \\(\\triangle\\) TQR. - Mathemerize","og_description":"Solution : Given,\u00a0 (QRover QS) = (QTover PR) So, (QTover QR) = (PRover QS)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;&#8230;.(1) Also given,\u00a0 (angle) 1 = (angle) 2 Since, sides opposite to equal (angle)s are equal, So , PR = PQ\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 &#8230;&#8230;&#8230;(2) From (1) and (2), we get (QTover &hellip; In the figure, (QRover QS) = (QTover PR) and (angle) 1 = (angle) 2. Show that (triangle) PQS ~ (triangle) TQR. Read More &raquo;","og_url":"https:\/\/mathemerize.com\/in-the-figure-qrover-qs-qtover-pr-and-angle-1-angle-2-show-that-triangle-pqs-triangle-tqr\/","og_site_name":"Mathemerize","article_published_time":"2022-07-07T14:35:42+00:00","article_modified_time":"2022-07-07T14:35:47+00:00","og_image":[{"url":"https:\/\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-3-4-300x201.jpeg"}],"author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/in-the-figure-qrover-qs-qtover-pr-and-angle-1-angle-2-show-that-triangle-pqs-triangle-tqr\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/in-the-figure-qrover-qs-qtover-pr-and-angle-1-angle-2-show-that-triangle-pqs-triangle-tqr\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"In the figure, \\(QR\\over QS\\) = \\(QT\\over PR\\) and \\(\\angle\\) 1 = \\(\\angle\\) 2. 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