{"id":148562,"date":"2024-10-04T20:51:24","date_gmt":"2024-10-04T20:51:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=148562"},"modified":"2024-10-04T20:51:27","modified_gmt":"2024-10-04T20:51:27","slug":"triangle-qrs-is-a-right-triangle","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/04\/triangle-qrs-is-a-right-triangle\/","title":{"rendered":"Triangle QRS is a right triangle"},"content":{"rendered":"\n<p>Triangle QRS is a right triangle. Complete the similarity statement. \u0394STR ~ \u0394<br>TQR<br>RST<br>SQR<br>RTQ<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The Correct Answer is :<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-3-color\"><strong>Delta SQR<\/strong><\/mark><\/p>\n\n\n\n<p>To complete the similarity statement ( \\Delta STR \\sim \\Delta TQR ), we need to understand the properties of similar triangles and how to determine which triangle corresponds to ( \\Delta TQR ).<\/p>\n\n\n\n<p>The triangles ( \\Delta STR ) and ( \\Delta TQR ) are stated to be similar. In similar triangles, corresponding angles are equal, and the lengths of corresponding sides are proportional. Since ( \\Delta QRS ) is a right triangle, let&#8217;s analyze the angles and sides involved.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Understanding Right Triangles<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In a right triangle, one angle is ( 90^\\circ ). Let&#8217;s assume triangle ( QRS ) has angle ( Q ) as the right angle.<\/li>\n\n\n\n<li>Thus, angles ( R ) and ( S ) are the acute angles, which means they sum up to ( 90^\\circ ) since the angles in any triangle sum to ( 180^\\circ ).<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Identifying Corresponding Angles<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The similarity statement ( \\Delta STR \\sim \\Delta TQR ) implies that:\n<ul class=\"wp-block-list\">\n<li>Angle ( S ) in triangle ( STR ) corresponds to angle ( T ) in triangle ( TQR ).<\/li>\n\n\n\n<li>Angle ( R ) in triangle ( STR ) corresponds to angle ( Q ) in triangle ( TQR ) (the right angle).<\/li>\n\n\n\n<li>Angle ( T ) in triangle ( STR ) corresponds to angle ( R ) in triangle ( TQR ).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Completing the Statement<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Given the correspondence and the angles involved, triangle ( STR ) has its angles matched with angles in triangle ( TQR ).<\/li>\n\n\n\n<li>The missing triangle from the similarity statement is ( SQR ), which shares angles ( Q ) and ( R ) with triangle ( TQR ).<\/li>\n<\/ul>\n\n\n\n<p>Thus, the complete similarity statement is:<br>[<br>\\Delta STR \\sim \\Delta SQR<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>In geometric problems involving right triangles, the relationships between angles and sides become critical for establishing similarity. The triangles can be similar due to angle-angle (AA) similarity, where two angles of one triangle are equal to two angles of another triangle. This relationship allows us to confirm that if ( \\Delta STR ) and ( \\Delta TQR ) share common angles, they must maintain proportional sides as well.<\/p>\n\n\n\n<p>Understanding triangle similarity helps in various applications, including solving for unknown side lengths using ratios, and can also be fundamental in trigonometric applications. By recognizing that triangle ( SQR ) aligns with the angles of triangle ( TQR ), we conclude their similarity, reinforcing the foundational principles of geometry.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Triangle QRS is a right triangle. Complete the similarity statement. \u0394STR ~ \u0394TQRRSTSQRRTQ The Correct Answer and Explanation is : The Correct Answer is :Delta SQR To complete the similarity statement ( \\Delta STR \\sim \\Delta TQR ), we need to understand the properties of similar triangles and how to determine which triangle corresponds to [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","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":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-148562","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/148562","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=148562"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/148562\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=148562"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=148562"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=148562"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}