Given: \u22201 and \u22202 form a linear pair; m\u22202 + m\u22203 = 180 prove: \u22201 is congruent to \u22203<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n Given:<\/strong><\/p>\n\n\n\n To Prove:<\/strong> ( \u22201 \u2245 \u22203 ).<\/p>\n\n\n\n Proof:<\/strong><\/p>\n\n\n\n This proof demonstrates the relationship between angles in a linear pair and supplementary angles. A linear pair<\/strong> of angles occurs when two angles are adjacent and their non-common sides form a straight line. In this case, the sum of ( m\u22201 ) and ( m\u22202 ) is ( 180^\\circ ), as a straight line measures ( 180^\\circ ).<\/p>\n\n\n\n We also know from the given information that ( m\u22202 + m\u22203 = 180^\\circ ), indicating that ( \u22202 ) and ( \u22203 ) are supplementary. Supplementary angles are two angles whose measures sum to ( 180^\\circ ).<\/p>\n\n\n\n The key to the proof is realizing that both equations (Step 1 and Step 2) equal ( 180^\\circ ). This allows us to set ( m\u22201 + m\u22202 ) equal to ( m\u22202 + m\u22203 ). By subtracting ( m\u22202 ) (which is common to both equations), we isolate ( m\u22201 = m\u22203 ). Since equal angle measures indicate congruence, ( \u22201 ) is congruent to ( \u22203 ).<\/p>\n\n\n\n Thus, the proof relies on the properties of linear pairs and supplementary angles, as well as the transitive property of equality, to establish the congruence of ( \u22201 ) and ( \u22203 ).<\/p>\n","protected":false},"excerpt":{"rendered":" Given: \u22201 and \u22202 form a linear pair; m\u22202 + m\u22203 = 180 prove: \u22201 is congruent to \u22203 The Correct Answer and Explanation is: Proof: \u22201 \u2245 \u22203 Given: To Prove: ( \u22201 \u2245 \u22203 ). Proof: Explanation: This proof demonstrates the relationship between angles in a linear pair and supplementary angles. A linear […]<\/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-168302","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168302","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=168302"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168302\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168302"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168302"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168302"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Proof: \u22201 \u2245 \u22203<\/h3>\n\n\n\n
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Explanation:<\/h3>\n\n\n\n