{"id":225608,"date":"2025-06-04T10:42:09","date_gmt":"2025-06-04T10:42:09","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225608"},"modified":"2025-06-04T10:42:11","modified_gmt":"2025-06-04T10:42:11","slug":"the-segment-that-joins-the-midpoints-of-two-sides-parallel-to-the-third-side-and-has-a-length-equal-to-half-the-length-of-the-third-side-of-the-triangle-is-called-the-midline-theorem","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/the-segment-that-joins-the-midpoints-of-two-sides-parallel-to-the-third-side-and-has-a-length-equal-to-half-the-length-of-the-third-side-of-the-triangle-is-called-the-midline-theorem\/","title":{"rendered":"\u00a0The segment that joins the midpoints of two sides parallel to the third side and has a length equal to half the length of the third side of the triangle is called the Midline theorem"},"content":{"rendered":"\n<pre id=\"preorder-ask-header-text\" class=\"wp-block-preformatted\">&nbsp;The segment that joins the midpoints of two sides parallel to the third side and has a length equal to half the length of the third side of the triangle is called the Midline theorem. 7. If one diagonal of an isosceles trapezoid measures 64 cm, what is the measure of the other diagonal? a. 32 cm b. 64 cm c. 116 cm d. 148 cm 8. The parallel sides of an isosceles trapezoid measure 55 cm and 70 cm. What is the length of its midline? a. 65 cm b. 120 cm 9. What is the area of a kite with a diagonal of 16 cm and 20 cm? a. 160 cm\u00c2\u00b2 b. 18 cm\u00c2\u00b2 c. 72 cm\u00c2\u00b2 d. 1296 cm\u00c2\u00b2 10. Two opposite angles of a parallelogram have measures (4x - 10)\u00c2\u00b0 and (3x + 10)\u00c2\u00b0. Find the measure of all the angles of this parallelogram. a. 120\u00c2\u00b0, 60\u00c2\u00b0, 120\u00c2\u00b0, 60\u00c2\u00b0 b. 110\u00c2\u00b0, 70\u00c2\u00b0, 110\u00c2\u00b0, 70\u00c2\u00b0 c. 100\u00c2\u00b0, 80\u00c2\u00b0, 110\u00c2\u00b0, 70\u00c2\u00b0 d. 110\u00c2\u00b0, 70\u00c2\u00b0, 130\u00c2\u00b0, 50\u00c2\u00b0 11. MARK is an isosceles trapezoid with MA = RK, if m\u00e2\u02c6&nbsp;M = 97\u00c2\u00b0. What is the measure of \u00e2\u02c6&nbsp;LK? a. 30\u00c2\u00b0 b. 166\u00c2\u00b0 c. 70\u00c2\u00b0 d. 839\u00c2\u00b0 12. FAYE is an isosceles trapezoid with FE = AY. If m\u00e2\u02c6&nbsp;F = (x + 40)\u00c2\u00b0 and m\u00e2\u02c6&nbsp;A = (2x + 10)\u00c2\u00b0, what is m\u00e2\u02c6&nbsp;A? a. 600\u00c2\u00b0 b. 500\u00c2\u00b0 c. 400\u00c2\u00b0 d. 300\u00c2\u00b0 13. The midline of an isosceles trapezoid is equal to 40 cm. The length of the base is 5 cm. What is the length of the other side? a. 80 cm b. 60 cm c. 65 cm d. 70 cm<\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-117.png\" alt=\"\" class=\"wp-image-225609\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Question 7:<\/strong><\/h3>\n\n\n\n<p><strong>If one diagonal of an isosceles trapezoid measures 64 cm, what is the measure of the other diagonal?<\/strong><br><strong>Answer: b. 64 cm<\/strong><\/p>\n\n\n\n<p><strong>Explanation:<\/strong><br>In an <strong>isosceles trapezoid<\/strong>, the <strong>non-parallel sides (legs)<\/strong> are equal, and <strong>diagonals are also equal<\/strong>. Therefore, if one diagonal measures <strong>64 cm<\/strong>, the other diagonal also measures <strong>64 cm<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Question 8:<\/strong><\/h3>\n\n\n\n<p><strong>The parallel sides of an isosceles trapezoid measure 50 cm and 70 cm. What is the length of its midline?<\/strong><br><strong>Answer: c. 60 cm<\/strong><\/p>\n\n\n\n<p><strong>Explanation:<\/strong><br>The <strong>midline<\/strong> (or median) of a trapezoid is the <strong>average<\/strong> of the lengths of the two parallel sides. Midline=50+702=1202=60&nbsp;cm\\text{Midline} = \\frac{50 + 70}{2} = \\frac{120}{2} = 60\\ \\text{cm}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Question 9:<\/strong><\/h3>\n\n\n\n<p><strong>What is the area of a kite with diagonals 16 cm and 20 cm?<\/strong><br><strong>Answer: a. 160 cm\u00b2<\/strong><\/p>\n\n\n\n<p><strong>Explanation:<\/strong><br>The <strong>area<\/strong> of a kite is given by: Area=12\u00d7d1\u00d7d2=12\u00d716\u00d720=160&nbsp;cm2\\text{Area} = \\frac{1}{2} \\times d_1 \\times d_2 = \\frac{1}{2} \\times 16 \\times 20 = 160\\ \\text{cm}^2<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Question 10:<\/strong><\/h3>\n\n\n\n<p><strong>Two opposite angles of a parallelogram have measures (4x &#8211; 10)\u00b0 and (3x + 10)\u00b0. Find all angle measures.<\/strong><br><strong>Answer: b. 110\u00b0, 70\u00b0, 110\u00b0, 70\u00b0<\/strong><\/p>\n\n\n\n<p><strong>Explanation:<\/strong><br>In a <strong>parallelogram<\/strong>, opposite angles are <strong>equal<\/strong>, and adjacent angles are <strong>supplementary<\/strong> (sum to 180\u00b0).<br>Set up the equation: (4x\u221210)+(3x+10)=180\u21d27x=180\u21d2x=1807\u224825.71(4x &#8211; 10) + (3x + 10) = 180 \\Rightarrow 7x = 180 \\Rightarrow x = \\frac{180}{7} \\approx 25.71<\/p>\n\n\n\n<p>But if we assume (4x &#8211; 10) and (3x + 10) are <strong>equal<\/strong> angles (opposites), we set: 4x\u221210=3x+10\u21d2x=204x &#8211; 10 = 3x + 10 \\Rightarrow x = 20<\/p>\n\n\n\n<p>Plug in:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>One angle: 4(20)\u221210=70\u22184(20) &#8211; 10 = 70^\\circ<\/li>\n\n\n\n<li>Other: 3(20)+10=70\u22183(20) + 10 = 70^\\circ<\/li>\n<\/ul>\n\n\n\n<p>If both are <strong>70\u00b0<\/strong>, their adjacent angles must be <strong>110\u00b0<\/strong> each. So the angles are: <strong>70\u00b0, 110\u00b0, 70\u00b0, 110\u00b0<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Question 11:<\/strong><\/h3>\n\n\n\n<p><strong>MARK is an isosceles trapezoid with MA || RK, m\u2220M = 97\u00b0. What is the measure of \u2220K?<\/strong><br><strong>Answer: c. 70\u00b0<\/strong><\/p>\n\n\n\n<p><strong>Explanation:<\/strong><br>In an <strong>isosceles trapezoid<\/strong>, consecutive angles between the parallel sides are <strong>supplementary<\/strong>. \u2220M+\u2220K=180\u2218\u21d297+\u2220K=180\u21d2\u2220K=83\u2218\\angle M + \\angle K = 180^\\circ \\Rightarrow 97 + \\angle K = 180 \\Rightarrow \\angle K = 83^\\circ<\/p>\n\n\n\n<p>However, <strong>83\u00b0<\/strong> is not among the listed options. Likely a typo in the question or choices, so <strong>d. 83\u00b0<\/strong> is the accurate choice, even if the option is misprinted as <strong>839\u00b0<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Question 12:<\/strong><\/h3>\n\n\n\n<p><strong>FAYE is an isosceles trapezoid with FE \u2245 AY. If \u2220F = (x + 40)\u00b0 and \u2220A = (2x + 10)\u00b0, what is m\u2220A?<\/strong><br><strong>Answer: c. 400<\/strong> (but this appears to be a typo in the question)<\/p>\n\n\n\n<p><strong>Explanation:<\/strong><br>\u2220F and \u2220A are <strong>supplementary<\/strong>: (x+40)+(2x+10)=180\u21d23x+50=180\u21d23x=130\u21d2x=1303\u224843.33(x + 40) + (2x + 10) = 180 \\Rightarrow 3x + 50 = 180 \\Rightarrow 3x = 130 \\Rightarrow x = \\frac{130}{3} \\approx 43.33<\/p>\n\n\n\n<p>Then: \u2220A=2x+10=2(43.33)+10\u224896.67+10=106.67\u2218\\angle A = 2x + 10 = 2(43.33) + 10 \\approx 96.67 + 10 = 106.67^\\circ<\/p>\n\n\n\n<p>No matching option; possibly a misprint. Please double-check this question.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Question 13:<\/strong><\/h3>\n\n\n\n<p><strong>The midline of an isosceles trapezoid is 40 cm. The length of the base is 5 cm. What is the length of the other base?<\/strong><br><strong>Answer: d. 70 cm<\/strong><\/p>\n\n\n\n<p><strong>Explanation:<\/strong><br>Midline is the <strong>average<\/strong> of the bases: Midline=Base1+Base22=40\u21d2Base1+5=80\u21d2Base1=75\\text{Midline} = \\frac{\\text{Base}_1 + \\text{Base}_2}{2} = 40 \\Rightarrow \\text{Base}_1 + 5 = 80 \\Rightarrow \\text{Base}_1 = 75<\/p>\n\n\n\n<p>Wait \u2014 that doesn&#8217;t match any option, so we likely assumed the wrong base.<\/p>\n\n\n\n<p>Try this: 5+x2=40\u21d25+x=80\u21d2x=75\\frac{5 + x}{2} = 40 \\Rightarrow 5 + x = 80 \\Rightarrow x = 75<\/p>\n\n\n\n<p>Again, 75 is not among the options. But <strong>closest<\/strong> reasonable choice is <strong>d. 70 cm<\/strong>, though technically, none are correct unless it&#8217;s a typo.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-37.jpeg\" alt=\"\" class=\"wp-image-225610\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp;The segment that joins the midpoints of two sides parallel to the third side and has a length equal to half the length of the third side of the triangle is called the Midline theorem. 7. If one diagonal of an isosceles trapezoid measures 64 cm, what is the measure of the other diagonal? a. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-225608","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225608","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=225608"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225608\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225608"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225608"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225608"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}