{"id":248624,"date":"2025-07-08T14:24:13","date_gmt":"2025-07-08T14:24:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=248624"},"modified":"2025-07-08T14:24:15","modified_gmt":"2025-07-08T14:24:15","slug":"worksheet-in-mathematics-8-grade-section","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/08\/worksheet-in-mathematics-8-grade-section\/","title":{"rendered":"Worksheet in Mathematics 8 Grade & Section"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Of course. Here are the correct answers for the worksheet, followed by a detailed explanation.<\/p>\n\n\n\n

Correct Answers<\/strong><\/h3>\n\n\n\n
    \n
  1. AC \u2245\u00a0DF<\/strong><\/li>\n\n\n\n
  2. AB \u2245\u00a0DE<\/strong><\/li>\n\n\n\n
  3. BC \u2245\u00a0EF<\/strong><\/li>\n\n\n\n
  4. \u2220A \u2245\u00a0\u2220D<\/strong><\/li>\n\n\n\n
  5. \u2220D \u2245\u00a0\u2220A<\/strong><\/li>\n\n\n\n
  6. \u2220B \u2245\u00a0\u2220E<\/strong><\/li>\n\n\n\n
  7. \u25b3CBL \u2245\u00a0\u25b3FED<\/strong>\u00a0(assuming CBL is a typo for CBA)<\/em><\/li>\n\n\n\n
  8. \u25b3DFE \u2245\u00a0\u25b3ACB<\/strong><\/li>\n\n\n\n
  9. \u25b3BAC \u2245\u00a0\u25b3EDF<\/strong><\/li>\n\n\n\n
  10. \u25b3EDF \u2245\u00a0\u25b3BAC<\/strong><\/li>\n<\/ol>\n\n\n\n

    Explanation<\/strong><\/h3>\n\n\n\n

    The key to solving this worksheet lies in understanding the initial congruence statement: \u25b3ABC \u2245 \u25b3DEF<\/strong>. This single line provides all the information needed to determine how the two triangles correspond to each other. In geometry, the order of the letters in a congruence statement is critical because it tells you exactly which vertices, angles, and sides match up.<\/p>\n\n\n\n

    From \u25b3ABC \u2245 \u25b3DEF<\/strong>, we can establish the following correspondence:<\/p>\n\n\n\n

      \n
    • The first vertex,\u00a0A<\/strong>, corresponds to the first vertex,\u00a0D<\/strong>.<\/li>\n\n\n\n
    • The second vertex,\u00a0B<\/strong>, corresponds to the second vertex,\u00a0E<\/strong>.<\/li>\n\n\n\n
    • The third vertex,\u00a0C<\/strong>, corresponds to the third vertex,\u00a0F<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      This principle is often called “Corresponding Parts of Congruent Triangles are Congruent” (CPCTC).<\/p>\n\n\n\n

      Solving for Sides and Angles (Questions 1-6):<\/strong>
      We apply this correspondence to find the congruent parts.<\/p>\n\n\n\n

        \n
      • For the sides: The side connecting vertices A and C (AC) must be congruent to the side connecting the corresponding vertices D and F (DF). Similarly, side AB corresponds to DE, and side BC corresponds to EF.<\/li>\n\n\n\n
      • For the angles: The angle at vertex A (\u2220A) must be congruent to the angle at the corresponding vertex D (\u2220D). Likewise, \u2220B is congruent to \u2220E, and \u2220C is congruent to \u2220F.<\/li>\n<\/ul>\n\n\n\n

        Solving for Triangle Congruence (Questions 7-10):<\/strong>
        The same logic extends to naming the entire triangle. The order of vertices must match the established correspondence.<\/p>\n\n\n\n

          \n
        • For question 9,\u00a0\u25b3BAC<\/strong>, we look at the corresponding vertices in order: B corresponds to E, A corresponds to D, and C corresponds to F. Therefore, \u25b3BAC is congruent to\u00a0\u25b3EDF<\/strong>.<\/li>\n\n\n\n
        • For question 8,\u00a0\u25b3DFE<\/strong>, we find the matches: D corresponds to A, F corresponds to C, and E corresponds to B. This means \u25b3DFE is congruent to\u00a0\u25b3ACB<\/strong>.<\/li>\n\n\n\n
        • Question 7 contains a likely typographical error, listing a point “L” that does not exist. Assuming it meant to be\u00a0\u25b3CBA<\/strong>, the corresponding vertices are F, E, and D, making it congruent to\u00a0\u25b3FED<\/strong>.<\/li>\n<\/ul>\n\n\n\n
          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

          The Correct Answer and Explanation is: Of course. Here are the correct answers for the worksheet, followed by a detailed explanation. Correct Answers Explanation The key to solving this worksheet lies in understanding the initial congruence statement: \u25b3ABC \u2245 \u25b3DEF. This single line provides all the information needed to determine how the two triangles correspond to […]<\/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-248624","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248624","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=248624"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248624\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=248624"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=248624"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=248624"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}