{"id":72043,"date":"2021-02-08T14:34:33","date_gmt":"2021-02-08T09:04:33","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=72043"},"modified":"2021-02-08T14:34:36","modified_gmt":"2021-02-08T09:04:36","slug":"rd-sharma-chapter-9-class-9-maths-exercise-9-1-solutions","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-9-class-9-maths-exercise-9-1-solutions\/","title":{"rendered":"RD Sharma Chapter 9 Class 9 Maths Exercise 9.1 Solutions"},"content":{"rendered":"\n<p>RD Sharma Chapter 9 Class 9 Maths Exercise 9.1 Solutions is based on the <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-9-triangle-and-its-angles\/\" target=\"_blank\" rel=\"noopener noreferrer\">Triangle and its Angle<\/a>. This chapter helps learn about the different angles of triangles like- Scalene Triangle, Acute Triangle, Right Triangle, Isosceles Triangle, etc. This exercise of Chapter 9 also includes the Angle sum property of a triangle. Here we will explain the triangles with a complete stepwise explanation and examples.<\/p>\n<p>Moreover, for practicing more, we have attached the free PDF for the students in which several questions are mentioned with the easy solutions. With the help of PDF, learners will get to know the variety of questions of Triangles and its angle. So, download RD Sharma Chapter 9 Class 9 Maths Exercise 9.1 Solutions PDF for free and start practicing to score well in the exam.<\/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-69d2d68969ede\" 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-69d2d68969ede\"><\/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-9-class-9-maths-exercise-9-1-solutions\/#download-rd-sharma-chapter-9-class-9-maths-exercise-91-solutions-pdf\" title=\"Download RD Sharma Chapter 9 Class 9 Maths Exercise 9.1 Solutions PDF\">Download RD Sharma Chapter 9 Class 9 Maths Exercise 9.1 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-9-class-9-maths-exercise-9-1-solutions\/#important-definitions-rd-sharma-chapter-9-class-9-maths-exercise-91-solutions\" title=\"Important Definitions RD Sharma Chapter 9 Class 9 Maths Exercise 9.1 Solutions\">Important Definitions RD Sharma Chapter 9 Class 9 Maths Exercise 9.1 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-9-class-9-maths-exercise-9-1-solutions\/#types-of-triangles\" title=\"Types of Triangles\">Types of Triangles<\/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-9-class-9-maths-exercise-9-1-solutions\/#triangles-on-the-basis-of-lengths-of-their-sides\" title=\"Triangles On the Basis of lengths of their Sides\">Triangles On the Basis of lengths of their Sides<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-9-class-9-maths-exercise-9-1-solutions\/#scalene-triangle\" title=\"Scalene Triangle\">Scalene Triangle<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-9-class-9-maths-exercise-9-1-solutions\/#isosceles-triangle\" title=\"Isosceles Triangle\">Isosceles Triangle<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-9-class-9-maths-exercise-9-1-solutions\/#equilateral-triangles\" title=\"Equilateral Triangles\">Equilateral Triangles<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-9-class-9-maths-exercise-9-1-solutions\/#triangles-on-the-basis-of-their-interior-angles\" title=\"Triangles On the Basis of Their Interior Angles\">Triangles On the Basis of Their Interior Angles<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-9-class-9-maths-exercise-9-1-solutions\/#obtuse-angled-triangle\" title=\"Obtuse Angled Triangle\">Obtuse Angled Triangle<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-9-class-9-maths-exercise-9-1-solutions\/#acute-angled-triangle\" title=\"Acute Angled Triangle\">Acute Angled Triangle<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-9-class-9-maths-exercise-9-1-solutions\/#right-angled-triangle\" title=\"Right Angled Triangle\">Right Angled Triangle<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-9-class-9-maths-exercise-9-1-solutions\/#angle-sum-property-of-a-triangle\" title=\"Angle Sum Property of a Triangle\">Angle Sum Property of a Triangle<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-9-class-9-maths-exercise-9-1-solutions\/#prove-an-angle-sum-property-of-a-triangle\" title=\"Prove An Angle Sum Property of a Triangle\">Prove An Angle Sum Property of a Triangle<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-chapter-9-class-9-maths-exercise-91-solutions-pdf\"><\/span>Download RD Sharma Chapter 9 Class 9 Maths Exercise 9.1 Solutions PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\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\/2021\/01\/Solutions-for-Class-9-Maths-Chapter-9-Triangle-and-its-Angles-Exercise-9.1.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/Solutions-for-Class-9-Maths-Chapter-9-Triangle-and-its-Angles-Exercise-9.1.pdf\">Solutions for Class 9 Maths Chapter 9 Triangle and its Angles Exercise 9.1<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"important-definitions-rd-sharma-chapter-9-class-9-maths-exercise-91-solutions\"><\/span>Important Definitions RD Sharma Chapter 9 Class 9 Maths Exercise 9.1 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>List of the topics and subtopics of Triangles and their angles-<\/p>\n<ol>\n<li>Types of triangles<\/li>\n<\/ol>\n<ul>\n<li>Scalene triangle<\/li>\n<li>Isosceles triangle<\/li>\n<li>Equilateral triangle<\/li>\n<li>Acute Triangle<\/li>\n<li>Right Angle Triangle<\/li>\n<li>Obtuse Triangle<\/li>\n<\/ul>\n<ol>\n<li>Angle sum property of a triangle<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"types-of-triangles\"><\/span><strong>Types of Triangles<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Triangles are classified into two types-<\/p>\n<ol>\n<li>On the basis of lengths of their sides (Scalene, Isosceles, Equilateral)<\/li>\n<li>On the basis of their interior angles (Obtuse, Acute, Right)<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"triangles-on-the-basis-of-lengths-of-their-sides\"><\/span><strong>Triangles On the Basis of lengths of their Sides<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The examples and definitions of the triangles based on the lengths of their sides are mentioned below in the following points.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"scalene-triangle\"><\/span><strong>Scalene Triangle<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>A scalene triangle has each side length of different measures. No side is equal in length to any of the other sides. Every interior angle is also different in the scalene triangle.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"isosceles-triangle\"><\/span><strong>Isosceles Triangle<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>In an Isosceles Triangle, the measures (length) of two of the three sides are equal. So, the angles opposite the corresponding sides are equivalent to each other. In simple words, it has two equal sides and two equal angles.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"equilateral-triangles\"><\/span><strong>Equilateral Triangles<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>In an equilateral triangle, the lengths of the sides are equivalent. Each of the interior angles has a length of 60 degrees. Considering the angles of an equilateral triangle are the same, it is also called an equiangular triangle.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"triangles-on-the-basis-of-their-interior-angles\"><\/span><strong>Triangles On the Basis of Their Interior Angles<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Please look at the example and definitions of the triangle based on their Interior Angles in the following points.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"obtuse-angled-triangle\"><\/span><strong>Obtuse Angled Triangle<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>In Obtuse triangles, one of the three interior angles has a length greater than 90 degrees. In simple words, if one of the angles in a triangle is an obtuse angle, so the triangle is known as an obtuse-angled triangle.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"acute-angled-triangle\"><\/span><strong>Acute Angled Triangle<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>A triangle whose all three interior angles are acute is known as an Acute Triangle. In simple words, if each interior angle is less than 90 degrees, so it is called an acute-angled triangle.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"right-angled-triangle\"><\/span><strong>Right Angled Triangle<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>A right triangle has one angle of 90 degrees. In a right-angled triangle, the side opposite to the right angle is the longest side known as the hypotenuse. As we have come across types of triangles with combined names like- a right isosceles triangle and so on, but this only signifies that the triangle has two equal sides with one of the interior angles remaining 90 degrees.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"angle-sum-property-of-a-triangle\"><\/span><strong>Angle Sum Property of a Triangle<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>An Angle sum property of a triangle signifies that the total of interior angles is 180\u00b0.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"prove-an-angle-sum-property-of-a-triangle\"><\/span><strong>Prove An Angle Sum Property of a Triangle<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Theorem 1- Prove that sum of each three-angle is 180\u00b0 or 2 right angles.<\/strong><\/p>\n<p><strong>Solution-<\/strong><\/p>\n<p>Given, \u2206PQR<\/p>\n<p>To prove: \u2220P + \u2220Q + \u2220R = 180\u00b0<\/p>\n<p>Draw AB || QR passes through point P.<\/p>\n<p>Proof: \u22201 = \u2220Q and \u22203 = \u2220R \u2026. (i)<\/p>\n<p>[ alternate angles \u2235 AB || QR]<\/p>\n<p>= APB is a line<\/p>\n<p>= \u22201 + \u22202 + \u22203 = 180\u00b0 (linear pair application)<\/p>\n<p>\u2220Q + \u22202 + \u2220R = 180\u00b0<\/p>\n<p>\u2220Q + \u2220RPQ + \u2220R = 180\u00b0<\/p>\n<p>= 2 right angles (Hence Proved).<\/p>\n<p><strong>Theorem 2- If one side of a triangle is given, then the exterior angle so set is equivalent to the sum of two interior opposite angles.<\/strong><\/p>\n<p><strong>Means \u22204 = \u22201 + \u22202<\/strong><\/p>\n<p><strong>Solution-<\/strong><\/p>\n<p>Given, Means \u22204 = \u22201 + \u22202<\/p>\n<p>= \u22203 = 180\u00b0 \u2013 (\u22201 + \u22202) &#8230;(1) (by an angle sum property) where, PQR is a line<\/p>\n<p>= \u22203 + \u22204 = 180\u00b0 (linear pair)<\/p>\n<p>= or \u22203 = 180\u00b0 \u2013 \u22204 &#8230;(2)<\/p>\n<p>=by (1) &amp; (2)<\/p>\n<p>= 180\u00b0 \u2013 (\u22201 + \u22202) = 180\u00b0 \u2013 \u22204<\/p>\n<p>= \u22201 + \u22202 = \u22204 (Hence Proved).<\/p>\n<p><a href=\"https:\/\/cbse.gov.in\/\" target=\"_blank\" rel=\"noopener noreferrer\">Know about CBSE Details<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>RD Sharma Chapter 9 Class 9 Maths Exercise 9.1 Solutions is based on the Triangle and its Angle. This chapter helps learn about the different angles of triangles like- Scalene Triangle, Acute Triangle, Right Triangle, Isosceles Triangle, etc. This exercise of Chapter 9 also includes the Angle sum property of a triangle. Here we will &#8230; <a title=\"RD Sharma Chapter 9 Class 9 Maths Exercise 9.1 Solutions\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-9-class-9-maths-exercise-9-1-solutions\/\" aria-label=\"More on RD Sharma Chapter 9 Class 9 Maths Exercise 9.1 Solutions\">Read more<\/a><\/p>\n","protected":false},"author":241,"featured_media":74009,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2985,2917,73719,73411,73410],"tags":[3081,3086,3085],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72043"}],"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=72043"}],"version-history":[{"count":3,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72043\/revisions"}],"predecessor-version":[{"id":74010,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72043\/revisions\/74010"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/74009"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=72043"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=72043"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=72043"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}