{"id":227518,"date":"2025-06-06T07:34:57","date_gmt":"2025-06-06T07:34:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=227518"},"modified":"2025-06-06T07:35:00","modified_gmt":"2025-06-06T07:35:00","slug":"which-statements-about-the-diagram-are-true","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/06\/which-statements-about-the-diagram-are-true\/","title":{"rendered":"Which statements about the diagram are true"},"content":{"rendered":"\n<p> Which statements about the diagram are true? Select three options. DE + EF > DF \\triangle DEF is an isosceles triangle. 5 &lt; DF &lt; 13 DE + DF &lt; EF \\triangle DEF is a scalene triangle<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-204.png\" alt=\"\" class=\"wp-image-227519\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is<\/mark><\/strong>:<\/p>\n\n\n\n<p>Based on the triangle diagram shown and the question, we are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>DE=4DE = 4DE=4 units<\/li>\n\n\n\n<li>EF=9EF = 9EF=9 units<\/li>\n\n\n\n<li>DFDFDF is unknown, but it is marked as congruent to DEDEDE, meaning DF=4DF = 4DF=4 units<\/li>\n\n\n\n<li>We are to choose <strong>three<\/strong> true statements.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-step Analysis:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Statement: DE + EF > DF<\/strong> Plug in the values:<br>DE+EF=4+9=13DE + EF = 4 + 9 = 13DE+EF=4+9=13<br>DF=4DF = 4DF=4<br>Since 13>413 > 413>4, this is <strong>true<\/strong>.<\/li>\n\n\n\n<li><strong>Statement: \u25b3DEF is an isosceles triangle.<\/strong> DE=DF=4DE = DF = 4DE=DF=4, and EF=9EF = 9EF=9. Since two sides are equal, triangle DEF is <strong>isosceles<\/strong>.<br>This is <strong>true<\/strong>.<\/li>\n\n\n\n<li><strong>Statement: 5 &lt; DF &lt; 13<\/strong> We already know DF=4DF = 4DF=4, so this statement becomes:<br>5&lt;4&lt;135 &lt; 4 &lt; 135&lt;4&lt;13, which is <strong>false<\/strong>.<\/li>\n\n\n\n<li><strong>Statement: DE + DF &lt; EF<\/strong> DE+DF=4+4=8DE + DF = 4 + 4 = 8DE+DF=4+4=8, and EF=9EF = 9EF=9<br>8&lt;98 &lt; 98&lt;9, so this is <strong>true<\/strong>.<\/li>\n\n\n\n<li><strong>Statement: \u25b3DEF is a scalene triangle.<\/strong> A scalene triangle has all sides of different lengths. Since DE=DF=4DE = DF = 4DE=DF=4, it is <strong>not<\/strong> scalene.<br>This is <strong>false<\/strong>.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Correct Answers:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>DE + EF > DF<\/strong><\/li>\n\n\n\n<li><strong>\u25b3DEF is an isosceles triangle<\/strong><\/li>\n\n\n\n<li><strong>DE + DF &lt; EF<\/strong><\/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\">Explanation<\/h3>\n\n\n\n<p>The triangle shown in the diagram is labeled \u25b3DEF\\triangle DEF\u25b3DEF, with side lengths DE=4DE = 4DE=4, EF=9EF = 9EF=9, and DF=4DF = 4DF=4. Because two of its sides are equal in length (DE=DFDE = DFDE=DF), the triangle is classified as <strong>isosceles<\/strong>, not scalene. A scalene triangle requires all three sides to be of different lengths, which is not the case here.<\/p>\n\n\n\n<p>The inequality DE+EF&gt;DFDE + EF &gt; DFDE+EF&gt;DF holds because 4+9=134 + 9 = 134+9=13, and 13&gt;413 &gt; 413&gt;4. This aligns with the <strong>Triangle Inequality Theorem<\/strong>, which states that the sum of any two sides of a triangle must be greater than the third side. Similarly, the inequality DE+DF&lt;EFDE + DF &lt; EFDE+DF&lt;EF evaluates to 4+4=84 + 4 = 84+4=8, and since 8&lt;98 &lt; 98&lt;9, this is also a valid and <strong>true<\/strong> statement.<\/p>\n\n\n\n<p>On the other hand, the statement 5&lt;DF&lt;135 &lt; DF &lt; 135&lt;DF&lt;13 is incorrect because DF=4DF = 4DF=4, which does not satisfy 5&lt;DF5 &lt; DF5&lt;DF. Therefore, this option is <strong>false<\/strong>. Additionally, since two sides of the triangle are equal, the triangle cannot be scalene, making the final statement false as well.<\/p>\n\n\n\n<p>In summary, the three correct and true statements based on the diagram and triangle properties are:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>DE+EF>DFDE + EF > DFDE+EF>DF<\/li>\n\n\n\n<li>\u25b3DEF\\triangle DEF\u25b3DEF is an isosceles triangle.<\/li>\n\n\n\n<li>DE+DF&lt;EFDE + DF &lt; EFDE+DF&lt;EF<\/li>\n<\/ol>\n\n\n\n<p>These conclusions are grounded in both direct measurements and geometric principles.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner9-99.jpeg\" alt=\"\" class=\"wp-image-227520\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Which statements about the diagram are true? Select three options. DE + EF > DF \\triangle DEF is an isosceles triangle. 5 &lt; DF &lt; 13 DE + DF &lt; EF \\triangle DEF is a scalene triangle The Correct Answer and Explanation is: Based on the triangle diagram shown and the question, we are given: [&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-227518","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227518","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=227518"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227518\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=227518"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=227518"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=227518"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}