{"id":9037,"date":"2020-12-04T09:29:32","date_gmt":"2020-12-04T03:59:32","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=9037"},"modified":"2020-12-04T15:14:00","modified_gmt":"2020-12-04T09:44:00","slug":"theorems-dealing-trapezoids","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/theorems-dealing-trapezoids\/","title":{"rendered":"Theorems Dealing with Trapezoids"},"content":{"rendered":"<h2><span style=\"color: #00ccff;\">Theorems Dealing with Trapezoids<\/span><\/h2>\n<h3><span style=\"color: #0000ff;\">Trapezoid<\/span><\/h3>\n<p><strong>Definition:<\/strong> A trapezoid is a quadrilateral with exactly one pair of parallel sides.<\/p>\n<p><strong>Trapezoid<\/strong> has only one set of parallel sides.<br \/>\n[The median of a trapezoid is parallel to the bases and equal to one-half the sum of the bases.]<\/p>\n<p>A trapezoid has ONLY ONE set of parallel sides.<br \/>\nWhen proving a figure is a trapezoid, it is necessary to prove that two sides are parallel and two sides are NOT parallel.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-124012 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/Theorems-Dealing-with-Trapezoids-1.jpg\" alt=\"Theorems Dealing with Trapezoids 1\" width=\"237\" height=\"194\" \/>The median (also called the mid-segment) of a trapezoid is a segment that connects the midpoint of one leg to the midpoint of the other leg.<\/p>\n<p><strong>Theorem:<\/strong> The median (or mid-segment) of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.<br \/>\n(True for ALL trapezoids.)<\/p>\n<h3><span style=\"color: #0000ff;\">Isosceles Trapezoid<\/span><\/h3>\n<p><strong>Definition:<\/strong> An isosceles trapezoid is a trapezoid with congruent legs.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-124013 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/Theorems-Dealing-with-Trapezoids-2.jpg\" alt=\"Theorems Dealing with Trapezoids 2\" width=\"235\" height=\"147\" \/><\/p>\n<p><strong>Properties:<\/strong><\/p>\n<ul>\n<li>Isosceles Trapezoid has only one set of parallel sides<\/li>\n<li>base angles congruent<\/li>\n<li>legs congruent<\/li>\n<li>diagonals congruent<\/li>\n<li>opposite angles supplementary<\/li>\n<\/ul>\n<p><strong>Theorems:<\/strong><\/p>\n<ol>\n<li>A trapezoid is isosceles if and only if the base angles are congruent.<\/li>\n<li>A trapezoid is isosceles if and only if the diagonals are congruent.<\/li>\n<li>If a trapezoid is isosceles, the opposite angles are supplementary.<\/li>\n<\/ol>\n<p>Never assume that a trapezoid is isosceles unless you are given (or can prove) that information.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Theorems Dealing with Trapezoids Trapezoid Definition: A trapezoid is a quadrilateral with exactly one pair of parallel sides. Trapezoid has only one set of parallel sides. [The median of a trapezoid is parallel to the bases and equal to one-half the sum of the bases.] A trapezoid has ONLY ONE set of parallel sides. When &#8230; <a title=\"Theorems Dealing with Trapezoids\" class=\"read-more\" href=\"https:\/\/cbselibrary.com\/theorems-dealing-trapezoids\/\" aria-label=\"More on Theorems Dealing with Trapezoids\">Read more<\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[3303],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v18.4.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Theorems Dealing with Trapezoids - CBSE Library<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cbselibrary.com\/theorems-dealing-trapezoids\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Theorems Dealing with Trapezoids\" \/>\n<meta property=\"og:description\" content=\"Theorems Dealing with Trapezoids Trapezoid Definition: A trapezoid is a quadrilateral with exactly one pair of parallel sides. 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