{"id":228816,"date":"2025-06-07T16:08:43","date_gmt":"2025-06-07T16:08:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228816"},"modified":"2025-06-07T16:08:45","modified_gmt":"2025-06-07T16:08:45","slug":"which-of-the-following-statements-must-be-true-based-on-the-diagram-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/which-of-the-following-statements-must-be-true-based-on-the-diagram-below\/","title":{"rendered":"Which of the following statements must be true based on the diagram below"},"content":{"rendered":"\n


Which of the following statements must be true based on the diagram below? (Diagram is not to scale ) BF is a segment bisector. Bis the vertex of a pair of congruent angles in the diagram Fis the vertex of a pair of congruent angles in the diagram Bis the midpoint ofa segment in the diagram: F is the midpoint of a segment in the diagram<\/p>\n\n\n\n

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

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

The correct answer is: F is the midpoint of a segment in the diagram.<\/strong><\/p>\n\n\n\n

\n\n\n\n

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

From the diagram, we observe triangle DBCDBCDBC with a point FFF on segment DCDCDC, and segment BFBFBF connecting point BBB to point FFF. The key visual clues are the tick marks<\/strong> on segments DFDFDF and FCFCFC, which indicate that:DF\u2245FCDF \\cong FCDF\u2245FC<\/p>\n\n\n\n

This tells us that point FFF<\/strong> divides segment DCDCDC into two congruent parts<\/strong>, meaning:F is the midpoint of DC\u203e.F \\text{ is the midpoint of } \\overline{DC}.F is the midpoint of DC.<\/p>\n\n\n\n

So the only statement that must be true based on the diagram<\/strong> is:<\/p>\n\n\n\n

\u2705 F is the midpoint of a segment in the diagram.<\/strong><\/p>\n\n\n\n

\n\n\n\n

Why the Other Choices Are Incorrect:<\/h3>\n\n\n\n
    \n
  1. BF is a segment bisector.<\/strong>\n
      \n
    • There is no information showing that BFBFBF bisects any other segment. No angles or segments are marked to indicate that BFBFBF cuts another segment into equal parts.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • B is the vertex of a pair of congruent angles in the diagram.<\/strong>\n
        \n
      • There are no angle congruence markings at vertex BBB. We cannot assume angle congruence just by visual estimation.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • F is the vertex of a pair of congruent angles in the diagram.<\/strong>\n
          \n
        • Again, no angle congruence is indicated at point FFF, only segment congruence.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • B is the midpoint of a segment in the diagram.<\/strong>\n
            \n
          • There is no indication that point BBB divides any segment into two equal parts.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
            \n\n\n\n

            Summary:<\/h3>\n\n\n\n

            The only marked congruence is between segments DFDFDF and FCFCFC, which shows that FFF is the midpoint<\/strong> of segment DCDCDC. All other options cannot be confirmed solely from the given diagram. Therefore, the correct and must-be-true<\/strong> statement is:<\/p>\n\n\n\n

            “F is the midpoint of a segment in the diagram.”<\/strong><\/p>\n\n\n\n

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

            Which of the following statements must be true based on the diagram below? (Diagram is not to scale ) BF is a segment bisector. Bis the vertex of a pair of congruent angles in the diagram Fis the vertex of a pair of congruent angles in the diagram Bis the midpoint ofa segment in the […]<\/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-228816","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228816","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=228816"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228816\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=228816"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=228816"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=228816"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}