Rhombus | Brilliant Math & Science Wiki

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class="alternative"> <p> Already have an account? <a href="https://brilliant.org/account/login/?next=/wiki/rhombus/" class="ax-click" data-ax-id="clicked_signup_modal_login" data-ax-type="link"> Log in here. </a> </p> </div> </div> </div> <div class="wiki-top-editors" id="cmp_wiki_top_editors_id"> <b>Jarry S</b>, <b>Dr. Bela Palnitkar</b>, and <b>Jimin Khim</b> contributed </div> <div id="wiki-main" data-controller="app/newsfeed:feed"> <div class="summary-container" id="cmp_wiki_canonical_page_id"> <div class="summary wiki-content" data-controller="app/wiki:summary,app/zoomable:images" data-cmp-url="/wiki/rhombus/" data-page-key="wiki_canonical_page" data-cmp-key="wiki_canonical_page"> <div class="section collapsed" id="section-pre-header-section"><div class="section-container"><p>A <strong>rhombus</strong> is a parallelogram in which all sides are equal. It's much more basic than a parallelogram and has the opposite properties of a <a target="_blank" rel="nofollow" href="https://brilliant.org/wiki/properties-of-rectangles/?subtopic=polygons&amp;chapter=quadrilaterals">rectangle</a>. (I do not have all the properties and information on this subject since I am in a college prep geometry class, so I would appreciate it if someone would add information and review my work. Note that I do not know the area and perimeter properties.)</p> <p>The definition of a <strong>rhombus</strong> is as follows:</p> <blockquote class="definition"><p>A <strong>rhombus</strong> is a quadrilateral whose sides are all equal.</blockquote> </p> <p><span class="image-caption center"> <img src="https://ds055uzetaobb.cloudfront.net/brioche/uploads/dhOSNWF1pB-rhombus-properties.png?width=1200" srcset="https://ds055uzetaobb.cloudfront.net/brioche/uploads/dhOSNWF1pB-rhombus-properties.png?width=1200 1x,https://ds055uzetaobb.cloudfront.net/brioche/uploads/dhOSNWF1pB-rhombus-properties.png?width=2400 2x,https://ds055uzetaobb.cloudfront.net/brioche/uploads/dhOSNWF1pB-rhombus-properties.png?width=3600 3x" alt="" /> </span> </p> <p>Notice that the diagonals are perpendicular and the sum of the perpendicular angles is \( 360^\circ \).</p> <blockquote> <p><strong>Property 1.</strong> All pairs of the consecutive sides of a rhombus are congruent. </p> <p><strong>Property 2.</strong> The diagonals of a rhombus are perpendicular.</p> </blockquote> <p>Remember, if a <strong>quadrilateral</strong> is both a <strong>rectangle</strong> and a <strong>rhombus</strong>, then it is a <a target="_blank" rel="nofollow" href="https://brilliant.org/wiki/properties-of-squares/?subtopic=polygons&amp;chapter=quadrilaterals">square</a>.</p> <p>Since all rhombuses are <a target="_blank" rel="nofollow" href="https://brilliant.org/wiki/parallelogram/#properties-of-parallelograms">parallelograms</a>, but not all parallelograms are rhombuses, a rhombus follows some of the rules that a parallelogram does. The following properties apply to parallelograms and rhombuses: </p> <blockquote> <p><strong>Property 3.</strong> One diagonal of a rhombus bisects a pair of opposite angles.</p> <p><strong>Property 4.</strong> The opposite sides of a rhombus are parallel.</p> </blockquote> </div> </div> </div> </div> </div> <div class="wiki-self-citation" data-controller="app/wiki:getCitationTime"> <strong>Cite as:</strong> Rhombus. <em>Brilliant.org</em>. 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