{"id":73918,"date":"2021-02-08T14:38:11","date_gmt":"2021-02-08T09:08:11","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=73918"},"modified":"2021-02-08T14:38:14","modified_gmt":"2021-02-08T09:08:14","slug":"rd-sharma-chapter-15-class-9-maths-exercise-15-3-solutions","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-15-class-9-maths-exercise-15-3-solutions\/","title":{"rendered":"RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions"},"content":{"rendered":"\n<p>RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions is about the topics Parallelogram on the same base and within the same parallels, mainly a parallelogram and triangles, which is concerned under the Area of Parallelograms and Triangles. Learners will get to know- \u201chow to compute the area of any quadrilateral which contains triangles.\u201d A detailed explanation is provided for each problem mentioned in the attached PDF with this article.<\/p>\n<p>The RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions PDF is prepared by our subject experts by analyzing RD Sharma, Previous Year\u2019s Question Paper, and CBSE Text Book of Class 9. Look down to the article to get more information on the topics and subtopics of this exercise.<\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-15-areas-of-parallelograms-and-triangles\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Learn about RD Sharma Class 9 Chapter 15 (Areas Of Parallelograms And Triangles)<\/strong><\/a><\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69d2951e141c2\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-69d2951e141c2\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-15-class-9-maths-exercise-15-3-solutions\/#download-rd-sharma-chapter-15-class-9-maths-exercise-153-solutions-pdf\" title=\"Download RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions PDF\">Download RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-15-class-9-maths-exercise-15-3-solutions\/#important-definitions-rd-sharma-chapter-15-class-9-maths-exercise-153-solutions\" title=\"Important Definitions RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions\">Important Definitions RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-15-class-9-maths-exercise-15-3-solutions\/#a-parallelogram-on-the-same-base-and-within-the-same-parallels\" title=\"A parallelogram on the same base and within the same parallels\">A parallelogram on the same base and within the same parallels<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-15-class-9-maths-exercise-15-3-solutions\/#examples-of-rd-sharma-chapter-15-class-9-maths-exercise-153-solutions\" title=\"Examples of RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions\">Examples of RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-15-class-9-maths-exercise-15-3-solutions\/#frequently-asked-question-faqs-of-rd-sharma-chapter-15-class-9-maths-exercise-153-solutions\" title=\"Frequently Asked Question (FAQs) of RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions\">Frequently Asked Question (FAQs) of RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-chapter-15-class-9-maths-exercise-153-solutions-pdf\"><\/span>Download RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2020\/11\/RD-Sharma-Class-9-Maths-Chapter-15.pdf\">RD Sharma Class 9 Maths Chapter 15<\/a><\/p>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2020\/11\/RD-Sharma-Class-9-Maths-Chapter-15.pdf\", \"#example1\");<\/script><\/p>\n<h2><span class=\"ez-toc-section\" id=\"important-definitions-rd-sharma-chapter-15-class-9-maths-exercise-153-solutions\"><\/span>Important Definitions RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"a-parallelogram-on-the-same-base-and-within-the-same-parallels\"><\/span><strong>A parallelogram on the same base and within the same parallels<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Suppose two parallelograms ABCD and ABEF, on the same base \u2018AB,\u2019 and between the same parallels, as shown below-<\/p>\n<p><img class=\"alignnone size-full wp-image-73919\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/02\/14.4-1-1.png\" alt=\"RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions\" width=\"448\" height=\"346\" \/><\/p>\n<p><strong>Theorem- <\/strong>A Parallelogram on the same base and between the same parallels are equal in area.<\/p>\n<p>Proof of a theorem-<\/p>\n<p>Consider the figure presented above. We can see the \u0394BCE and \u0394ADF are congruent (similar). We have-<\/p>\n<ul>\n<li>BC = AD (opposing sides of a parallelogram are similar)<\/li>\n<li>\u2220BCE = \u2220ADF (Corresponding Angles)<\/li>\n<li>\u2220BEC = \u2220AFD (Corresponding Angles)<\/li>\n<\/ul>\n<p>By the ASA criterion, the two triangles are congruent, which means that their areas are equal. Now,<\/p>\n<p>= Area (ABCD) = Area (ABED) + Area (\u0394BCE)<\/p>\n<p>Then,<\/p>\n<p>= Area (ABEF) = Area (ABED) + Area (\u0394ADF)<\/p>\n<p>So,<\/p>\n<p>= Area (ABCD) = Area (ABEF)<\/p>\n<p>Hence Proved that a parallelogram on the same base and between the same parallels.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"examples-of-rd-sharma-chapter-15-class-9-maths-exercise-153-solutions\"><\/span><strong>Examples of RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Ques- In the figure, ABCD is a trapezium in which AB = 7cm, AD = BC = 5cm, DC = xcm, and the distance between AB and DC is 4cm. Find the value of \u2018x\u2019 and area of trapezium \u2018ABCD\u2019.<\/p>\n<p><img class=\"alignnone size-full wp-image-73920\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/02\/15.3-2.png\" alt=\"RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions\" width=\"750\" height=\"432\" \/><\/p>\n<p>Solution-<\/p>\n<p>Given- ABCD is a trapezium, where AB = 7cm, AD = BC = 5cm, DC = xcm, and<\/p>\n<p>The distance between AB and DC = 4cm<\/p>\n<p>Suppose AL and BM are perpendiculars on DC, then.<\/p>\n<p>= AL = BM = 4cm and LM = 7cm.<\/p>\n<p>In right \u0394BMC-<\/p>\n<p>By Applying Pythagorean Theorem, we get-<\/p>\n<p>= BC2 = BM2 + MC2<\/p>\n<p>= 25 = 16 + MC2<\/p>\n<p>= MC2 = 25 \u2013 16 = 9<\/p>\n<p>= or MC = 3<\/p>\n<p>Again,<\/p>\n<p>In right \u0394 ADL-<\/p>\n<p>By Applying Pythagorean Theorem, we get-<\/p>\n<p>= AD2 = AL2 + DL2<\/p>\n<p>= 25 = 16 + DL2<\/p>\n<p>= DL2 = 25 \u2013 16 = 9<\/p>\n<p>= or DL = 3<\/p>\n<p>Therefore, x = DC = DL + LM + MC = 3 + 7 + 3 = 13<\/p>\n<p>= x = 13cm<\/p>\n<p>Now,<\/p>\n<p>Area of trapezium ABCD = 1\/2(AB + CD) AL<\/p>\n<p>= 1\/2(7+13)4<\/p>\n<p>= 40<\/p>\n<p>Area of trapezium ABCD is 40cm2<\/p>\n<h2><span class=\"ez-toc-section\" id=\"frequently-asked-question-faqs-of-rd-sharma-chapter-15-class-9-maths-exercise-153-solutions\"><\/span>Frequently Asked Question (FAQs) of RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Ques 1- Can a parallelogram be separated into two triangles?<\/p>\n<p>Ans- As per the theorem of parallelogram-<\/p>\n<ol>\n<li>Each diagonal of a parallelogram bisects (divides) the parallelogram into two similar (congruent) triangles.<\/li>\n<li>The opposite edges\/ sides of a parallelogram are similar (congruent).<\/li>\n<\/ol>\n<p>Ques 2- What is diagonal in a triangle?<\/p>\n<p>Ans- The diagonal in a triangle is known as Regular Polygon.<\/p>\n<p>A triangle has no diagonals. A square has two diagonals of the same length, which cross at the center of the square.<\/p>\n<p><a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Know about CBSE Board<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions is about the topics Parallelogram on the same base and within the same parallels, mainly a parallelogram and triangles, which is concerned under the Area of Parallelograms and Triangles. Learners will get to know- \u201chow to compute the area of any quadrilateral which contains triangles.\u201d &#8230; <a title=\"RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-15-class-9-maths-exercise-15-3-solutions\/\" aria-label=\"More on RD Sharma Chapter 15 Class 9 Maths Exercise 15.3 Solutions\">Read more<\/a><\/p>\n","protected":false},"author":241,"featured_media":73921,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2917,73719,73411,2985],"tags":[3081,3086,3085],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/73918"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/241"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=73918"}],"version-history":[{"count":2,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/73918\/revisions"}],"predecessor-version":[{"id":74015,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/73918\/revisions\/74015"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/73921"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=73918"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=73918"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=73918"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}