{"id":286,"date":"2022-04-13T04:45:32","date_gmt":"2022-04-13T04:45:32","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=286"},"modified":"2024-11-22T07:19:36","modified_gmt":"2024-11-22T07:19:36","slug":"o-7-properties-of-rhombuses","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/o-7-properties-of-rhombuses\/","title":{"rendered":"O.7 Properties of rhombuses"},"content":{"rendered":"\n

Properties of rhombuses<\/strong><\/h2>\n\n\n\n

Key Notes:<\/p>\n\n\n\n

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Each diagonal of a rhombus bisects a pair of congruent opposite angles. Also, consecutive angles in a rhombus are supplementary.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Learn with an example<\/strong><\/p>\n\n\n\n

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Quadrilateral STUV is a rhombus. What is \u2220SUV?<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n<\/div><\/div>\n\n\n\n

Since STUV is a rhombus, \u2220TUV and \u2220SVU are supplementary.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Set the sum of their measures equal to 180\u00b0 and plug in \u2220SVU to solve for \u2220TUV.<\/p>\n\n\n\n

\u2220SVU+\u2220TUV=180\u00b0<\/p>\n\n\n\n

128\u00b0<\/strong>+\u2220TUV=180\u00b0 Plug in \u2220SVU=128\u00b0<\/p>\n\n\n\n

\u2220TUV=52\u00b0 Subtract 128\u00b0 from both sides<\/p>\n\n\n\n

Also, SU bisects \u2220TUV, so \u2220SUV=\u2220SUT=12\u2220TUV. Next, plug in \u2220TUV=52\u00b0 to this equation and solve for \u2220SUV.<\/p>\n\n\n\n

\u2220SUV=12\u2220TUV<\/p>\n\n\n\n

=12(52\u00b0<\/strong>) Plug in \u2220TUV=52\u00b0<\/p>\n\n\n\n

=26\u00b0 Multiply<\/p>\n\n\n\n

So, \u2220SUV=26\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n

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Quadrilateral GHIJ is a rhombus. What is \u2220FIH?<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n<\/div><\/div>\n\n\n\n

Since GHIJ is a rhombus, opposite angles are congruent, GI bisects \u2220HIJ, and HJ bisects \u2220GJI.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

So, \u2220FJG\u2245\u2220FJI\u2245\u2220FHG\u2245\u2220FHI and \u2220FGH\u2245\u2220FGJ\u2245\u2220FIH\u2245\u2220FIJ. Specifically \u2220FHI=\u2220FJG=33\u00b0. Also, since GI and HJ are perpendicular, \u2220HFI=90\u00b0 and \u25b3FHI is a right triangle.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

This means \u2220FHI and \u2220FIH are complementary. Set the sum of their measures equal to 90\u00b0 and plug in \u2220FHI=33\u00b0 to solve for \u2220FIH.<\/p>\n\n\n\n

\u2220FHI+\u2220FIH=90\u00b0<\/p>\n\n\n\n

33\u00b0<\/strong>+\u2220FIH=90\u00b0 Plug in \u2220FHI=33\u00b0<\/p>\n\n\n\n

\u2220FIH=57\u00b0 Subtract 33\u00b0 from both sides<\/p>\n\n\n\n

So, \u2220FIH=57\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n

\n
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Quadrilateral GHIJ is a rhombus. What is \u2220FJG?<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n<\/div><\/div>\n\n\n\n

Since GHIJ is a rhombus, opposite angles are congruent, GI bisects \u2220HIJ, and HJ bisects \u2220GJI<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

So, \u2220FIH\u2245\u2220FIJ\u2245\u2220FGH\u2245\u2220FGJ and \u2220FHG\u2245\u2220FHI\u2245\u2220FJG\u2245\u2220FJI. Specifically \u2220FGJ=\u2220FIH=32\u00b0. Also, since GI and HJ are perpendicular, \u2220GFJ=90\u00b0 and \u25b3FGJ is a right triangle.<\/p>\n\n\n\n

\"\"<\/figure>\n<\/div><\/div>\n\n\n\n

let’s practice!<\/p>\n<\/div><\/div>\n\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n\n
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\"\"<\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Properties of rhombuses Key Notes: Each diagonal of a rhombus bisects a pair of congruent opposite angles. Also, consecutive angles in a rhombus are supplementary. Learn with an example Quadrilateral STUV is a rhombus. What is \u2220SUV? Since STUV is a rhombus, \u2220TUV and \u2220SVU are supplementary. Set the sum of their measures equal to 180\u00b0 and plug in \u2220SVU to solve for \u2220TUV. \u2220SVU+\u2220TUV=180\u00b0 128\u00b0+\u2220TUV=180\u00b0 Plug in \u2220SVU=128\u00b0 \u2220TUV=52\u00b0 Subtract 128\u00b0 from both sides Also, SU bisects \u2220TUV, so \u2220SUV=\u2220SUT=12\u2220TUV. Next,Continue reading “O.7 Properties of rhombuses”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-286","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/286","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=286"}],"version-history":[{"count":14,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/286\/revisions"}],"predecessor-version":[{"id":18655,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/286\/revisions\/18655"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=286"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}