{"id":31464,"date":"2025-06-22T02:44:12","date_gmt":"2025-06-22T02:44:12","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=31464"},"modified":"2025-06-22T02:44:15","modified_gmt":"2025-06-22T02:44:15","slug":"write-the-missing-reasons-to-complete-the-proof","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/write-the-missing-reasons-to-complete-the-proof\/","title":{"rendered":"Write the missing reasons to complete the proof"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"766\" height=\"620\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-174.png\" alt=\"\" class=\"wp-image-31465\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-174.png 766w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-174-300x243.png 300w\" sizes=\"auto, (max-width: 766px) 100vw, 766px\" \/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To complete the proof that \u0394FAC \u2245 \u0394EDB, the correct missing reasons are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Step 5 Reason<\/strong>: Addition Property of Equality<\/li>\n\n\n\n<li><strong>Step 8 Reason<\/strong>: SAS Congruence Postulate<\/li>\n<\/ul>\n\n\n\n<p>Here is a clear and structured explanation:<\/p>\n\n\n\n<p>The problem presents two triangles, \u0394FAC and \u0394EDB, and provides three congruent relationships: AB \u2245 CD, \u2220A \u2245 \u2220D, and AF \u2245 DE. We aim to prove that the two triangles are congruent.<\/p>\n\n\n\n<p>The proof begins with the three given facts: AF \u2245 DE, \u2220A \u2245 \u2220D, and AB \u2245 CD. These are the foundation for constructing congruent parts between the two triangles.<\/p>\n\n\n\n<p>In step 4, we assert that AB = CD. This follows from the definition of congruent segments, since congruent segments have equal length. In step 5, we state that AB + BC = CD + BC. This is justified using the Addition Property of Equality, which allows the same quantity to be added to both sides of an equation. Since AB = CD, adding BC to both gives equal sums.<\/p>\n\n\n\n<p>Step 6 claims AC = BD. This follows from the Segment Addition Postulate, which says that the length of a segment made by adding two connected segments equals the total length. Since AB + BC = AC and CD + BC = BD, their equality implies AC = BD.<\/p>\n\n\n\n<p>In step 7, we conclude AC \u2245 BD using the definition of congruent segments, since they have equal lengths.<\/p>\n\n\n\n<p>Finally, we apply the SAS Congruence Postulate in step 8. Triangles FAC and EDB each have two sides and the included angle congruent: AF \u2245 DE, \u2220A \u2245 \u2220D, and AC \u2245 BD. This satisfies the condition of the postulate and thus proves that the two triangles are congruent.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-158.jpeg\" alt=\"\" class=\"wp-image-31466\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-158.jpeg 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-158-300x300.jpeg 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-158-150x150.jpeg 150w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-158-768x768.jpeg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: To complete the proof that \u0394FAC \u2245 \u0394EDB, the correct missing reasons are: Here is a clear and structured explanation: The problem presents two triangles, \u0394FAC and \u0394EDB, and provides three congruent relationships: AB \u2245 CD, \u2220A \u2245 \u2220D, and AF \u2245 DE. We aim to prove that the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-31464","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/31464","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=31464"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/31464\/revisions"}],"predecessor-version":[{"id":31467,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/31464\/revisions\/31467"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=31464"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=31464"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=31464"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}