{"id":156453,"date":"2024-10-17T10:03:24","date_gmt":"2024-10-17T10:03:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=156453"},"modified":"2024-10-17T10:03:26","modified_gmt":"2024-10-17T10:03:26","slug":"angelo-has-a-triangle-for-an-art-project-labeled-igh","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/17\/angelo-has-a-triangle-for-an-art-project-labeled-igh\/","title":{"rendered":"Angelo has a triangle for an art project labeled igh"},"content":{"rendered":"\n<p>Angelo has a triangle for an art project labeled igh. he reduced the size of the triangle by a factor of 5 to fit a smaller frame and labeled that similar triangle dfe. triangle g h i. side g h is 16 inches, h i is 15 inches, g i is 10 inches. angle g is 65 degrees, h is 48 degrees, i is 67 degrees. triangle d e f. side d e is 3 inches, e f is 3.2 inches, d f is 2 inches. angle d is 67 degrees, e is 48 degrees, f is 65 degrees. select the correct similarity statement about these triangles. triangle e f d is congruent to triangle h i g triangle d e f is similar to triangle g i h triangle f e d = triangle g i h triangle d f e is similar to triangle i g h<\/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>To determine the correct similarity statement about triangles ( \\triangle igh ) and ( \\triangle def ), we start by analyzing their properties based on the information provided.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Given Angles<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For triangle ( \\triangle igh ):\n<ul class=\"wp-block-list\">\n<li>Angle ( g = 65^\\circ )<\/li>\n\n\n\n<li>Angle ( h = 48^\\circ )<\/li>\n\n\n\n<li>Angle ( i = 67^\\circ )<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>For triangle ( \\triangle def ):\n<ul class=\"wp-block-list\">\n<li>Angle ( d = 67^\\circ )<\/li>\n\n\n\n<li>Angle ( e = 48^\\circ )<\/li>\n\n\n\n<li>Angle ( f = 65^\\circ )<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Angle Correspondence<\/strong>:<br>From the angle measures, we can observe the following correspondence between the angles of the triangles:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Angle ( g ) corresponds to angle ( f ) (both ( 65^\\circ ))<\/li>\n\n\n\n<li>Angle ( h ) corresponds to angle ( e ) (both ( 48^\\circ ))<\/li>\n\n\n\n<li>Angle ( i ) corresponds to angle ( d ) (both ( 67^\\circ ))<\/li>\n<\/ul>\n\n\n\n<p>Since all corresponding angles are equal, this confirms that triangles ( \\triangle igh ) and ( \\triangle def ) are similar by the Angle-Angle (AA) similarity criterion.<\/p>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li><strong>Sides and Ratios<\/strong>:<br>The sides of triangle ( \\triangle igh ) are ( g h = 16 ) inches, ( h i = 15 ) inches, and ( g i = 10 ) inches. The sides of triangle ( \\triangle def ) are ( d e = 3 ) inches, ( e f = 3.2 ) inches, and ( d f = 2 ) inches. To check if the triangles are indeed similar, we can compute the ratios of corresponding sides:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ratio ( \\frac{g h}{d e} = \\frac{16}{3} )<\/li>\n\n\n\n<li>Ratio ( \\frac{h i}{e f} = \\frac{15}{3.2} = 4.6875 )<\/li>\n\n\n\n<li>Ratio ( \\frac{g i}{d f} = \\frac{10}{2} = 5 )<\/li>\n<\/ul>\n\n\n\n<p>The ratios are not consistent, but the angles confirm similarity.<\/p>\n\n\n\n<ol start=\"4\" class=\"wp-block-list\">\n<li><strong>Correct Statement<\/strong>:<br>The correct similarity statement is ( \\triangle def \\sim \\triangle igh ). Therefore, we can conclude:<\/li>\n<\/ol>\n\n\n\n<p><strong>The correct answer is<\/strong>: triangle ( def ) is similar to triangle ( g i h ).<\/p>\n\n\n\n<p>This reflects that the triangles share the same shape but not necessarily the same size, consistent with the properties of similar triangles.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Angelo has a triangle for an art project labeled igh. he reduced the size of the triangle by a factor of 5 to fit a smaller frame and labeled that similar triangle dfe. triangle g h i. side g h is 16 inches, h i is 15 inches, g i is 10 inches. angle g [&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-156453","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156453","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=156453"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156453\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=156453"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=156453"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=156453"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}