{"id":248620,"date":"2025-07-08T14:21:37","date_gmt":"2025-07-08T14:21:37","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=248620"},"modified":"2025-07-08T14:21:39","modified_gmt":"2025-07-08T14:21:39","slug":"using-visual-cues-complete-the-congruence-statements-for-the-two-right-triangles-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/08\/using-visual-cues-complete-the-congruence-statements-for-the-two-right-triangles-below\/","title":{"rendered":"Using Visual Cues Complete the congruence statements for the two right triangles below."},"content":{"rendered":"\n
Using Visual Cues Complete the congruence statements for the two right triangles below.<\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Of course. Here is the completed solution and a detailed explanation.<\/p>\n\n\n\n
Completed Congruence Statements<\/strong><\/h3>\n\n\n\n
Congruent Sides<\/strong>Generated code<\/p>\n\n\n\n
AB \u2245 DE\nBC \u2245 EF\nAC \u2245 DF<\/code><\/pre>\n\n\n\n
Congruent Angles<\/strong><\/p>\n\n\n\n
\u2220A \u2245 \u2220D   <-- This statement names the congruent right angles.\n\u2220B \u2245 \u2220E\n\u2220C \u2245 \u2220F<\/code><\/pre>\n\n\n\n
Explanation<\/strong><\/h3>\n\n\n\n
The problem requires us to identify the corresponding congruent sides and angles of the two right triangles, ABC and DEF, based on the provided visual cues and the given congruence statement, \u0394ABC \u2245 \u0394DEF.<\/p>\n\n\n\n
The statement \u0394ABC \u2245 \u0394DEF is the most important piece of information. It tells us that the two triangles are congruent and also specifies which vertices correspond to each other. The order of the letters is critical:<\/p>\n\n\n\n
    \n
  • A<\/strong>\u00a0corresponds to\u00a0D<\/strong>.<\/li>\n\n\n\n
  • B<\/strong>\u00a0corresponds to\u00a0E<\/strong>.<\/li>\n\n\n\n
  • C<\/strong>\u00a0corresponds to\u00a0F<\/strong>.<\/li>\n<\/ul>\n\n\n\n
    Using this correspondence, we can determine all the pairs of congruent parts. This principle is often referred to as “Corresponding Parts of Congruent Triangles are Congruent” (CPCTC).<\/p>\n\n\n\n
    Finding Congruent Sides:<\/strong>
    We match the vertices in pairs to find the congruent sides:<\/p>\n\n\n\n
      \n
    1. Side\u00a0AB<\/strong>\u00a0(first and second letters of \u0394ABC) corresponds to side\u00a0DE<\/strong>\u00a0(first and second letters of \u0394DEF). The diagram confirms this, showing both sides have a length of 12.<\/li>\n\n\n\n
    2. Side\u00a0BC<\/strong>\u00a0(second and third letters) corresponds to side\u00a0EF<\/strong>\u00a0(second and third letters). The diagram confirms this, as both are hypotenuses with a length of 13.<\/li>\n\n\n\n
    3. Side\u00a0AC<\/strong>\u00a0(first and third letters) corresponds to side\u00a0DF<\/strong>\u00a0(first and third letters). The diagram shows side AC has a length of 5, so side DF must also have a length of 5.<\/li>\n<\/ol>\n\n\n\n
      Finding Congruent Angles:<\/strong>
      We match the individual vertices to find the congruent angles:<\/p>\n\n\n\n
        \n
      1. Angle\u00a0A<\/strong>\u00a0(first letter) corresponds to Angle\u00a0D<\/strong>\u00a0(first letter). The diagram shows both are right angles, measuring 90\u00b0.<\/li>\n\n\n\n
      2. Angle\u00a0B<\/strong>\u00a0(second letter) corresponds to Angle\u00a0E<\/strong>\u00a0(second letter). The diagram confirms this, showing both angles measure 23\u00b0.<\/li>\n\n\n\n
      3. Angle\u00a0C<\/strong>\u00a0(third letter) corresponds to Angle\u00a0F<\/strong>\u00a0(third letter). The diagram confirms this, showing both angles measure 67\u00b0.<\/li>\n<\/ol>\n\n\n\n
        The final instruction is to identify the statement that names the congruent right angles. Since Angle A and Angle D both measure 90\u00b0, they are the right angles. Therefore, the correct statement is \u2220A \u2245 \u2220D.<\/p>\n\n\n\n
        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
        Using Visual Cues Complete the congruence statements for the two right triangles below. The Correct Answer and Explanation is: Of course. Here is the completed solution and a detailed explanation. Completed Congruence Statements Congruent SidesGenerated code Congruent Angles Explanation The problem requires us to identify the corresponding congruent sides and angles of the two right […]<\/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-248620","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248620","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=248620"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248620\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=248620"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=248620"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=248620"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}