{"id":225807,"date":"2025-06-04T15:50:34","date_gmt":"2025-06-04T15:50:34","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225807"},"modified":"2025-06-04T15:50:36","modified_gmt":"2025-06-04T15:50:36","slug":"use-the-diagram","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/use-the-diagram\/","title":{"rendered":"use the diagram"},"content":{"rendered":"\n

use the diagram. (See Example 2.) t B S A E C D 11. What is another name for \\overline{BD}? 12. What is another name for \\overline{AC}? 13. What is another name for ray \\overrightarrow{AE}? 14. Name all rays with endpoint E. 15. Name two pairs of opposite rays<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

Based on the provided diagram and the labeled points A,B,C,D,EA, B, C, D, E, and the lines and rays shown, here are the correct answers to Exercises 11\u201315, followed by a full explanation.<\/p>\n\n\n\n

\n\n\n\n

11. What is another name for BD\u203e\\overline{BD}?<\/strong><\/h3>\n\n\n\n

Answer:<\/strong> DB\u203e\\overline{DB}<\/p>\n\n\n\n

12. What is another name for AC\u203e\\overline{AC}?<\/strong><\/h3>\n\n\n\n

Answer:<\/strong> CA\u203e\\overline{CA}<\/p>\n\n\n\n

13. What is another name for ray AE\u2192\\overrightarrow{AE}?<\/strong><\/h3>\n\n\n\n

Answer:<\/strong> AS\u2192\\overrightarrow{AS}<\/p>\n\n\n\n

14. Name all rays with endpoint E.<\/strong><\/h3>\n\n\n\n

Answer:<\/strong><\/p>\n\n\n\n

    \n
  • EB\u2192\\overrightarrow{EB}<\/li>\n\n\n\n
  • ED\u2192\\overrightarrow{ED}<\/li>\n\n\n\n
  • EA\u2192\\overrightarrow{EA}<\/li>\n\n\n\n
  • EC\u2192\\overrightarrow{EC}<\/li>\n<\/ul>\n\n\n\n

    15. Name two pairs of opposite rays.<\/strong><\/h3>\n\n\n\n

    Answer:<\/strong><\/p>\n\n\n\n

      \n
    • EA\u2192\\overrightarrow{EA} and EC\u2192\\overrightarrow{EC}<\/li>\n\n\n\n
    • ED\u2192\\overrightarrow{ED} and EB\u2192\\overrightarrow{EB}<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

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

      In geometry, understanding lines, line segments, rays, and their relationships is essential for interpreting diagrams accurately.<\/p>\n\n\n\n

      For question 11<\/strong>, BD\u203e\\overline{BD} is a line segment connecting points B and D. Since line segments are not directional, the order of points does not matter. Thus, BD\u203e=DB\u203e\\overline{BD} = \\overline{DB}. Both represent the same segment.<\/p>\n\n\n\n

      In question 12<\/strong>, the same logic applies. Segment AC\u203e\\overline{AC} can also be written as CA\u203e\\overline{CA}, since the distance and endpoints are unchanged.<\/p>\n\n\n\n

      Question 13<\/strong> involves naming a ray. A ray starts at one point and extends infinitely in one direction. Ray AE\u2192\\overrightarrow{AE} begins at point A and passes through point E toward the right. Looking at the diagram, the ray AS\u2192\\overrightarrow{AS} also starts at A and moves in the same direction, since S lies on the same path before A, making it another name for the same ray.<\/p>\n\n\n\n

      For question 14<\/strong>, all rays with endpoint E include those extending from E through another point. From the diagram, E connects directly to B, D, A, and C, giving us rays EB\u2192\\overrightarrow{EB}, ED\u2192\\overrightarrow{ED}, EA\u2192\\overrightarrow{EA}, and EC\u2192\\overrightarrow{EC}.<\/p>\n\n\n\n

      Finally, question 15<\/strong> asks about opposite rays\u2014two rays that share the same endpoint and extend in exactly opposite directions forming a straight line. From the diagram:<\/p>\n\n\n\n

        \n
      • EA\u2192\\overrightarrow{EA} and EC\u2192\\overrightarrow{EC} are opposite rays on the horizontal line.<\/li>\n\n\n\n
      • ED\u2192\\overrightarrow{ED} and EB\u2192\\overrightarrow{EB} are opposite rays on the diagonal line.<\/li>\n<\/ul>\n\n\n\n

        Understanding these relationships helps develop spatial reasoning and accurate geometric labeling skills.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        use the diagram. (See Example 2.) t B S A E C D 11. What is another name for \\overline{BD}? 12. What is another name for \\overline{AC}? 13. What is another name for ray \\overrightarrow{AE}? 14. Name all rays with endpoint E. 15. Name two pairs of opposite rays The Correct Answer and Explanation is: […]<\/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-225807","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225807","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=225807"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225807\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225807"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225807"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225807"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}