{"id":224647,"date":"2025-06-03T10:35:57","date_gmt":"2025-06-03T10:35:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224647"},"modified":"2025-06-03T10:35:59","modified_gmt":"2025-06-03T10:35:59","slug":"the-diagram-shows-two-parallel-lines-cut-by-a-transversal","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/the-diagram-shows-two-parallel-lines-cut-by-a-transversal\/","title":{"rendered":"The diagram shows two parallel lines cut by a transversal."},"content":{"rendered":"\n
The diagram shows two parallel lines cut by a transversal. Which of the following angles must be congruent to \u22201? 5 6 7 8 1 2 3 4 \u22202 \u22206 \u22203 \u22207 \u22204 \u22208 \u22205<\/pre>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
The correct answer is \u22205<\/strong>.<\/p>\n\n\n\n
\n\n\n\n
Explanation <\/h3>\n\n\n\n
In the diagram, two parallel lines are intersected by a transversal line. This geometric setup creates several types of angle pairs, including corresponding angles<\/strong>, alternate interior angles<\/strong>, alternate exterior angles<\/strong>, and vertical angles<\/strong>.<\/p>\n\n\n\n
We are asked to find the angle that must be congruent to \u22201<\/strong>.<\/p>\n\n\n\n
First, observe that \u22201 and \u22205 are corresponding angles<\/strong>. Corresponding angles are located in the same relative position at each intersection where a transversal crosses parallel lines. Since the lines are parallel, corresponding angles are always congruent<\/strong>. Therefore, \u22201 \u2245 \u22205.<\/p>\n\n\n\n
Let\u2019s briefly examine the other options to understand why they are incorrect:<\/p>\n\n\n\n
    \n
  • \u22202<\/strong> is adjacent to \u22201 and forms a linear pair with it, making them supplementary<\/strong>, not congruent.<\/li>\n\n\n\n
  • \u22203<\/strong> is vertically opposite to \u22201, but because they are not formed by the same intersection (they are on different intersections of the transversal with the parallel lines), they are not vertical angles and not congruent.<\/li>\n\n\n\n
  • \u22204<\/strong> is also not corresponding, alternate interior, or vertical to \u22201.<\/li>\n\n\n\n
  • \u22206, \u22207, and \u22208<\/strong> are all in different positions relative to \u22201 and do not fall into any angle pair relationship with \u22201 that guarantees congruence.<\/li>\n<\/ul>\n\n\n\n
    Key Definitions:<\/h3>\n\n\n\n
      \n
    • Corresponding angles<\/strong>: Same relative position at each intersection.<\/li>\n\n\n\n
    • Alternate interior angles<\/strong>: Inside the parallel lines, on opposite sides of the transversal.<\/li>\n\n\n\n
    • Alternate exterior angles<\/strong>: Outside the parallel lines, on opposite sides of the transversal.<\/li>\n\n\n\n
    • Vertical angles<\/strong>: Opposite angles formed by two intersecting lines; always congruent.<\/li>\n<\/ul>\n\n\n\n
      In summary, since \u22201 and \u22205 are corresponding angles<\/strong> formed by a transversal intersecting two parallel lines<\/strong>, they are congruent by definition. So, the correct answer is:<\/p>\n\n\n\n
      \u2705 \u22205<\/strong>.<\/p>\n\n\n\n
      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
      The diagram shows two parallel lines cut by a transversal. Which of the following angles must be congruent to \u22201? 5 6 7 8 1 2 3 4 \u22202 \u22206 \u22203 \u22207 \u22204 \u22208 \u22205 The Correct Answer and Explanation is: The correct answer is \u22205. Explanation In the diagram, two parallel lines are intersected by a transversal line. This geometric setup creates […]<\/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-224647","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224647","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=224647"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224647\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224647"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224647"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224647"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}