{"id":143556,"date":"2022-07-17T23:43:30","date_gmt":"2022-07-17T18:13:30","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=143556"},"modified":"2022-06-30T15:01:26","modified_gmt":"2022-06-30T09:31:26","slug":"a-rhombus-is-a-parallelogram-whose-diagonals-meet-at-right-angles","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/a-rhombus-is-a-parallelogram-whose-diagonals-meet-at-right-angles\/","title":{"rendered":"A Rhombus is a Parallelogram whose Diagonals Meet at Right Angles Theorem &#038; Proof"},"content":{"rendered":"<p>It is easy to prove that a rhombus is a parallelogram whose diagonals meet at right angles. Let the two diagonals of a parallelogram intersect at a point O. If the angle at the point they meet is 90 degrees, then by using Pythagorean theorem each side of the rectangle.<\/p>\n<p>A parallelogram with all four equal sides and right angles is known as the rhombus. Here we will prove that &#8220;A Rhombus is a Parallelogram whose diagonals meet at right angles&#8221;. If the given figure has right angles then we can say that the given parallelogram is a Rhombus.<\/p>\n<p><strong>Also Read:<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/ccssanswers.com\/opposite-angles-of-a-parallelogram-are-equal\/\">Opposite Angles of a Parallelogram are Equal<\/a><\/li>\n<li><a href=\"https:\/\/ccssanswers.com\/diagonals-of-a-parallelogram-bisect-each-other\/\">Diagonals of a Parallelogram Bisect Each Other<\/a><\/li>\n<\/ul>\n<h2>A Rhombus is a Parallelogram whose Diagonals Meet at Right Angles<\/h2>\n<p><strong>Theorem:<\/strong><br \/>\nProve that A Rhombus is a <a href=\"https:\/\/ccssanswers.com\/parallelogram\/\">Parallelogram<\/a> whose Diagonals Meet at Right Angles<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-121541\" src=\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/ABCD-parallelogram_1-300x208.png\" alt=\"ABCD parallelogram_1\" width=\"300\" height=\"208\" \/><\/p>\n<p>Given:<br \/>\nConsider the parallelogram ABCD with diagonals AD and BC as shown in the above figure.<br \/>\nAnd the diagonals meet at the point &#8220;O&#8221;.<br \/>\nA parallelogram is a rhombus if its adjacent sides are equal.<br \/>\nConsider \u0394AOB and \u0394AOC<br \/>\n\u2220AOB = \u2220AOC [both 90\u00b0 because given that diagonals intersect at right angles]<br \/>\nOC = OB [diagonals of a parallelogram bisect each other]<br \/>\nAO is the common side<br \/>\n\u0394AOB \u2245 \u0394AOC<br \/>\nAB = AC [corresponding sides of congruent triangles]<br \/>\nThus the adjacent sides are equal.<br \/>\nTherefore, we can say that the parallelogram ABCD is a rhombus.<br \/>\nHence Proved<br \/>\nThus a parallelogram whose diagonals intersect at right angles is a rhombus.<\/p>\n<h3>FAQs on a Rhombus is a Parallelogram Diagonals Intersect at Right Angles<\/h3>\n<p><strong>1. Do the diagonals of a rhombus meet at right angles?<\/strong><\/p>\n<p>The diagonals of a rhombus bisect each other at right angles.<\/p>\n<p><strong>2. Do the diagonals of a parallelogram meet at a right angle?<\/strong><\/p>\n<p>No, as per the rule the diagonals of a parallelogram do not bisect each other at right angles. We know that a parallelogram is a quadrilateral with opposite sides parallel and equal in length. All parallelograms are not squares, the diagonals do not intersect at right angles.<\/p>\n<p><strong>3. Does a rhombus have right angles yes or no?<\/strong><\/p>\n<p>A square has parallel sides, four right angles, and four equal sides. A square can be a rectangle and a parallelogram. No, because a rhombus does not have to have four right angles.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>It is easy to prove that a rhombus is a parallelogram whose diagonals meet at right angles. Let the two diagonals of a parallelogram intersect at a point O. If the angle at the point they meet is 90 degrees, then by using Pythagorean theorem each side of the rectangle. A parallelogram with all four &#8230; <a title=\"A Rhombus is a Parallelogram whose Diagonals Meet at Right Angles Theorem &#038; Proof\" class=\"read-more\" href=\"https:\/\/ccssanswers.com\/a-rhombus-is-a-parallelogram-whose-diagonals-meet-at-right-angles\/\" aria-label=\"More on A Rhombus is a Parallelogram whose Diagonals Meet at Right Angles Theorem &#038; Proof\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/143556"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=143556"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/143556\/revisions"}],"predecessor-version":[{"id":143558,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/143556\/revisions\/143558"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=143556"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=143556"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=143556"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}