{"id":195631,"date":"2025-02-28T14:14:38","date_gmt":"2025-02-28T14:14:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=195631"},"modified":"2025-02-28T14:14:40","modified_gmt":"2025-02-28T14:14:40","slug":"substitution-congruent-supplements-theorem-law-of-syllogism","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/28\/substitution-congruent-supplements-theorem-law-of-syllogism\/","title":{"rendered":"Substitution Congruent Supplements Theorem Law of Syllogism"},"content":{"rendered":"\n

Substitution Congruent Supplements Theorem Law of Syllogism<\/p>\n\n\n\n

Linear Pairs Theorem Angle Addition Postulate Definition of Perpendicular Lines Definition of Linear Pair Vertical Angles Theorem Transitive Property of Equality<\/p>\n\n\n\n

                    Statement\n\n                   Reason<\/code><\/pre>\n\n\n\n
1<\/p>\n\n\n\n
WZX=WZV<\/p>\n\n\n\n
Given<\/p>\n\n\n\n
2<\/p>\n\n\n\n
WZX and WZV are a linear pair<\/p>\n\n\n\n
3<\/p>\n\n\n\n
MWZX + mWZV = 180\u00b0<\/p>\n\n\n\n
4<\/p>\n\n\n\n
MWZX +mWZX 180\u00b0<\/p>\n\n\n\n
5<\/p>\n\n\n\n
MWZX-90\u00b0<\/p>\n\n\n\n
Substraction property of equality<\/p>\n\n\n\n
6<\/p>\n\n\n\n
WY 1 VX<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n
\ue200i\ue202turn0image0\ue201To complete the given proof, we’ll provide the missing statements and reasons, ensuring each step logically follows from the previous one.<\/p>\n\n\n\n
Proof:<\/strong><\/p>\n\n\n\n
Statement<\/th>Reason<\/th><\/tr><\/thead>
1. \u2220WZX \u2245 \u2220WZV<\/td>Given<\/td><\/tr>
2. \u2220WZX and \u2220WZV are a linear pair.<\/td>Definition of Linear Pair<\/td><\/tr>
3. m\u2220WZX + m\u2220WZV = 180\u00b0<\/td>Linear Pair Theorem<\/td><\/tr>
4. m\u2220WZX + m\u2220WZX = 180\u00b0<\/td>Substitution (since \u2220WZX \u2245 \u2220WZV)<\/td><\/tr>
5. 2 \u00d7 m\u2220WZX = 180\u00b0<\/td>Simplification<\/td><\/tr>
6. m\u2220WZX = 90\u00b0<\/td>Division Property of Equality<\/td><\/tr>
7. WY \u22a5 VX<\/td>Definition of Perpendicular Lines (since \u2220WZX is 90\u00b0)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Explanation:<\/strong><\/p>\n\n\n\n
    \n
  1. Given:<\/strong> We start with the information that \u2220WZX is congruent to \u2220WZV.<\/li>\n\n\n\n
  2. Definition of Linear Pair:<\/strong> The angles \u2220WZX and \u2220WZV are stated to form a linear pair. By definition, a linear pair consists of two adjacent angles whose non-common sides form a straight line.<\/li>\n\n\n\n
  3. Linear Pair Theorem:<\/strong> Angles that form a linear pair are supplementary, meaning their measures add up to 180 degrees. Therefore, m\u2220WZX + m\u2220WZV = 180\u00b0.<\/li>\n\n\n\n
  4. Substitution:<\/strong> Since \u2220WZX is congruent to \u2220WZV, their measures are equal. We can substitute m\u2220WZV with m\u2220WZX in the equation from step 3, resulting in m\u2220WZX + m\u2220WZX = 180\u00b0.<\/li>\n\n\n\n
  5. Simplification:<\/strong> Combining like terms, we get 2 \u00d7 m\u2220WZX = 180\u00b0.<\/li>\n\n\n\n
  6. Division Property of Equality:<\/strong> To isolate m\u2220WZX, we divide both sides of the equation by 2, yielding m\u2220WZX = 90\u00b0.<\/li>\n\n\n\n
  7. Definition of Perpendicular Lines:<\/strong> An angle measuring 90 degrees is a right angle. If \u2220WZX is a right angle, then by definition, the lines WY and VX are perpendicular to each other.<\/li>\n<\/ol>\n\n\n\n
    This proof demonstrates that if two congruent angles form a linear pair, each must be a right angle, leading to the conclusion that the lines forming these angles are perpendicular.<\/p>\n","protected":false},"excerpt":{"rendered":"
    Substitution Congruent Supplements Theorem Law of Syllogism Linear Pairs Theorem Angle Addition Postulate Definition of Perpendicular Lines Definition of Linear Pair Vertical Angles Theorem Transitive Property of Equality 1 WZX=WZV Given 2 WZX and WZV are a linear pair 3 MWZX + mWZV = 180\u00b0 4 MWZX +mWZX 180\u00b0 5 MWZX-90\u00b0 Substraction property of equality […]<\/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-195631","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195631","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=195631"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195631\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=195631"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=195631"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=195631"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}