{"id":29272,"date":"2025-06-20T20:46:10","date_gmt":"2025-06-20T20:46:10","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=29272"},"modified":"2025-06-20T20:46:12","modified_gmt":"2025-06-20T20:46:12","slug":"which-of-the-following-is-a-step-towards-proving-the-similarity-of-triangles-idef-and-iged","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-of-the-following-is-a-step-towards-proving-the-similarity-of-triangles-idef-and-iged\/","title":{"rendered":"Which of the following is a step towards proving the similarity of triangles \u00ce\u201dDEF and \u00ce\u201dGED"},"content":{"rendered":"\n<p>In \u00ce\u201dDEF shown below, segment DG is an altitude: Triangle DEF with segment DG drawn from vertex D and intersecting side EF. Which of the following is a step towards proving the similarity of triangles \u00ce\u201dDEF and \u00ce\u201dGED? (6 points) Segment EF is a hypotenuse. Angle E is congruent to itself. Segment ED is shorter than segment EF. Segment EF is intersected by segment DG.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><br><strong>Angle E is congruent to itself.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>To prove that two triangles are similar, we need to establish that their corresponding angles are equal and that their corresponding sides are in proportion. One of the most common methods used to prove similarity is the <strong>Angle-Angle (AA) Similarity Postulate<\/strong>, which states that if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.<\/p>\n\n\n\n<p>In triangle <strong>DEF<\/strong>, segment <strong>DG<\/strong> is drawn from vertex <strong>D<\/strong> and intersects side <strong>EF<\/strong> at point <strong>G<\/strong>, forming a right angle. This makes <strong>DG<\/strong> an <strong>altitude<\/strong>, and creates two smaller triangles: <strong>triangle GED<\/strong> and <strong>triangle DEF<\/strong>.<\/p>\n\n\n\n<p>Since <strong>DG<\/strong> is an altitude, angle <strong>DGE<\/strong> is a right angle. Triangle <strong>DEF<\/strong> also contains this right angle because <strong>DG<\/strong> is perpendicular to side <strong>EF<\/strong>. Therefore, both triangles <strong>GED<\/strong> and <strong>DEF<\/strong> share a right angle.<\/p>\n\n\n\n<p>Next, look at <strong>angle E<\/strong>. It is a part of both triangle <strong>DEF<\/strong> and triangle <strong>GED<\/strong>. Since it is the exact same angle in both triangles, it is <strong>congruent to itself<\/strong>. This is a valid and important geometric reasoning called the <strong>Reflexive Property<\/strong> of angle congruence.<\/p>\n\n\n\n<p>By confirming that triangle <strong>DEF<\/strong> and triangle <strong>GED<\/strong> share two angles (the right angle at point G and angle E), we have met the conditions of the <strong>AA Similarity Postulate<\/strong>. Hence, triangles <strong>DEF<\/strong> and <strong>GED<\/strong> are similar.<\/p>\n\n\n\n<p>Now, examine the incorrect options:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>&#8220;Segment EF is a hypotenuse&#8221; does not help prove similarity directly.<\/li>\n\n\n\n<li>&#8220;Segment ED is shorter than segment EF&#8221; speaks about lengths, but not ratios or angles.<\/li>\n\n\n\n<li>&#8220;Segment EF is intersected by segment DG&#8221; is just a fact about the diagram, not a step in proving similarity.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the correct reasoning step is: <strong>Angle E is congruent to itself.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-160.jpeg\" alt=\"\" class=\"wp-image-29274\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-160.jpeg 722w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-160-212x300.jpeg 212w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>In \u00ce\u201dDEF shown below, segment DG is an altitude: Triangle DEF with segment DG drawn from vertex D and intersecting side EF. Which of the following is a step towards proving the similarity of triangles \u00ce\u201dDEF and \u00ce\u201dGED? (6 points) Segment EF is a hypotenuse. Angle E is congruent to itself. Segment ED is shorter [&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-29272","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/29272","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=29272"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/29272\/revisions"}],"predecessor-version":[{"id":29278,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/29272\/revisions\/29278"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=29272"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=29272"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=29272"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}