{"id":241722,"date":"2025-07-03T20:24:56","date_gmt":"2025-07-03T20:24:56","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=241722"},"modified":"2025-07-03T20:24:58","modified_gmt":"2025-07-03T20:24:58","slug":"state-what-additional-information-is-required-in-order-to-know-that-the-triangles-are-congruent-for-the-given-reason","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/03\/state-what-additional-information-is-required-in-order-to-know-that-the-triangles-are-congruent-for-the-given-reason\/","title":{"rendered":"State what additional information is required in order to know that the triangles are congruent for the given reason."},"content":{"rendered":"\n

Problem 2 Instructions: State what additional information is required in order to know that the triangles are congruent for the given reason. Given: AAS<\/p>\n\n\n\n

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

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

Correct Answer:<\/strong>
QP \u2245 HG<\/p>\n\n\n\n

\n\n\n\n

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

The problem requires us to identify the additional piece of information needed to prove that the two triangles, \u0394QRP and \u0394HIG, are congruent using the Angle-Angle-Side (AAS) Congruence Postulate.<\/p>\n\n\n\n

The AAS postulate states that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the two triangles are congruent. A non-included side is any side that is not directly between the two angles.<\/p>\n\n\n\n

First, let’s analyze the information already provided in the diagram. The angle markings indicate the following congruencies:<\/p>\n\n\n\n

    \n
  1. Angle (A):<\/strong>\u00a0The single arc in \u2220R and \u2220I shows that \u2220R \u2245 \u2220I.<\/li>\n\n\n\n
  2. Angle (A):<\/strong>\u00a0The double arcs in \u2220Q and \u2220H show that \u2220Q \u2245 \u2220H.<\/li>\n<\/ol>\n\n\n\n

    We now have the two “Angle” components required for the AAS postulate. The next step is to find the “Side” component. According to the AAS rule, this must be a non-included side.<\/p>\n\n\n\n

    In \u0394QRP, the given angles are \u2220Q and \u2220R. The side located between these two angles is side QR. This is the included<\/em> side. Therefore, the non-included sides are the other two sides: QP<\/strong> and RP<\/strong>.<\/p>\n\n\n\n

    In the second triangle, \u0394HIG, the given angles are \u2220H and \u2220I. The side located between them is HI, which is the included side. The non-included sides are HG<\/strong> and IG<\/strong>.<\/p>\n\n\n\n

    To use AAS, we must show that a pair of corresponding non-included sides are congruent. Based on the congruent angles, we can determine the corresponding vertices: Q corresponds to H, and R corresponds to I. This implies that the remaining vertices, P and G, also correspond.<\/p>\n\n\n\n

    Therefore, the corresponding non-included sides are:<\/p>\n\n\n\n

      \n
    • Side\u00a0QP<\/strong>\u00a0corresponds to side\u00a0HG<\/strong>.<\/li>\n\n\n\n
    • Side\u00a0RP<\/strong>\u00a0corresponds to side\u00a0IG<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      We need one of these pairs to be congruent. Thus, the additional information required could be either QP \u2245 HG or RP \u2245 IG. Selecting the first pair, we find that if we are given QP \u2245 HG<\/strong>, we can prove the triangles are congruent by AAS.<\/p>\n\n\n\n

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

      Problem 2 Instructions: State what additional information is required in order to know that the triangles are congruent for the given reason. Given: AAS The Correct Answer and Explanation is: Correct Answer:QP \u2245 HG Explanation The problem requires us to identify the additional piece of information needed to prove that the two triangles, \u0394QRP and […]<\/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-241722","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/241722","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=241722"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/241722\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=241722"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=241722"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=241722"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}