{"id":72857,"date":"2023-04-03T00:29:00","date_gmt":"2023-04-02T18:59:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=72857"},"modified":"2023-10-20T10:25:15","modified_gmt":"2023-10-20T04:55:15","slug":"rd-sharma-chapter-10-class-9-maths-exercise-10-6-solutions","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-10-class-9-maths-exercise-10-6-solutions\/","title":{"rendered":"RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions"},"content":{"rendered":"\n<p>RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions: As we have learned that if two sides of a triangle are equivalent to the angles opposite to them, they are also similar and vice-versa. In this RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions, we will learn about Some Inequality Relations in a Triangle.<\/p>\n<p>This topic is mainly concerned with the RHS (Right angle-Hypotenuse-Side) and its concept. According to the Inequality Relations in a Triangle, the total of two sides of a triangle is perpetually greater than the third side of a triangle. Through this exercise, students will get a stepwise explanation of each problem with an example.<\/p>\n<p>Furthermore, the PDF attached below helps students practice more with the variety of problems available. The questions are prepared by our experts using RD Sharma, the Previous Year\u2019s Question Paper, and Text Book of Class 9.<\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-10-congruent-triangles\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Learn about RD Sharma Class 9 Chapter 10 (Congruent 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-69e0c2694ffde\" 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-69e0c2694ffde\"><\/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-10-class-9-maths-exercise-10-6-solutions\/#download-rd-sharma-chapter-10-class-9-maths-exercise-106-solutions-pdf\" title=\"Download RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions PDF\">Download RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 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-10-class-9-maths-exercise-10-6-solutions\/#important-definitions-rd-sharma-chapter-10-class-9-maths-exercise-106-solutions\" title=\"Important Definitions RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions\">Important Definitions RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 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-10-class-9-maths-exercise-10-6-solutions\/#proof-of-theorem-of-triangle-inequality\" title=\"Proof of Theorem of Triangle Inequality\">Proof of Theorem of Triangle Inequality<\/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-10-class-9-maths-exercise-10-6-solutions\/#examples-of-rd-sharma-chapter-10-class-9-maths-exercise-106-solutions\" title=\"Examples of RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions\">Examples of RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 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-10-class-9-maths-exercise-10-6-solutions\/#faqs-on-rd-sharma-chapter-10-class-9-maths-exercise-106-solutions\" title=\"FAQs on RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions\">FAQs on RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-10-class-9-maths-exercise-10-6-solutions\/#from-where-can-i-download-the-pdf-of-rd-sharma-chapter-10-class-9-maths-exercise-106-solutions\" title=\"From where can I download the PDF of RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions?\">From where can I download the PDF of RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-10-class-9-maths-exercise-10-6-solutions\/#how-much-does-it-cost-to-download-the-pdf-of-rd-sharma-chapter-10-class-9-maths-exercise-106-solutions\" title=\"How much does it cost to download the PDF of RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions?\">How much does it cost to download the PDF of RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions?<\/a><\/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-10-class-9-maths-exercise-10-6-solutions\/#can-i-access-the-rd-sharma-chapter-10-class-9-maths-exercise-106-solutions-pdf-offline\" title=\"Can I access the RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions PDF offline?\">Can I access the RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions PDF offline?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-chapter-10-class-9-maths-exercise-106-solutions-pdf\"><\/span>Download RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 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\/02\/Solutions-for-Class-9-Maths-Chapter-10-Congruent-Triangles-Exercise-10.6.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/02\/Solutions-for-Class-9-Maths-Chapter-10-Congruent-Triangles-Exercise-10.6.pdf\">Solutions for Class 9 Maths Chapter 10 Congruent Triangles Exercise 10.6<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"important-definitions-rd-sharma-chapter-10-class-9-maths-exercise-106-solutions\"><\/span>Important Definitions RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>According to the theorem of Inequality Relations in a Triangle, for any triangle, the sum of two sides of a triangle is perpetually greater than the third side.<\/p>\n<ul>\n<li>A polygon surrounded by three line segments is called the Triangle. It is the least possible polygon.<\/li>\n<li>The triangle has three vertices, three sides, and three interior angles.<\/li>\n<li>The kinds of triangles are based on their angle measure and the length of the sides.<\/li>\n<li>The inequality theorem is appropriate for all triangles, such as isosceles triangles, equilateral triangles, and scalene triangles.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"proof-of-theorem-of-triangle-inequality\"><\/span><strong>Proof of Theorem of Triangle Inequality<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The theorem defines the relationship among the three sides of the triangle. According to this theorem, in any triangle, the total lengths of two sides are perpetually greater than the third side of a triangle. In simpler words, it defines that the smallest distance between two different points is always a straight line.<\/p>\n<p>Suppose an \u2206ABC as shown below, with a, b, and c as the side lengths.<\/p>\n<p><img class=\"alignnone size-full wp-image-72858 aligncenter\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/02\/10.6-2.png\" alt=\"RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions\" width=\"279\" height=\"254\" \/><\/p>\n<p>The triangle inequality theorem declares that-<\/p>\n<ul>\n<li>a &lt; b + c<\/li>\n<li>b &lt; a + c<\/li>\n<li>c &lt; a + b<\/li>\n<\/ul>\n<p>Any triangle that has the least distance from any vertex to the opposite side is Perpendicular. In the figure below, XP is the least line segment from vertex X to side YZ.<\/p>\n<p><img class=\"alignnone size-full wp-image-72859 aligncenter\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/02\/10.6-1.png\" alt=\"RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions\" width=\"428\" height=\"201\" \/><\/p>\n<p>Let\u2019s prove the theorem now for a triangle ABC.<\/p>\n<p><img class=\"alignnone size-full wp-image-72860 aligncenter\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/02\/10.6-3.png\" alt=\"RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions\" width=\"365\" height=\"148\" \/><\/p>\n<p>To Prove- |BC|&lt; |AB| + |AC|<\/p>\n<p><strong>Construction:<\/strong> Suppose an \u2206ABC. Increase the side AC to point D so that AD = AB, as shown in the following figure.<\/p>\n<p><img class=\"alignnone size-full wp-image-72861 aligncenter\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/02\/10.6-4.png\" alt=\"RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions\" width=\"384\" height=\"256\" \/><\/p>\n<table>\n<tbody>\n<tr>\n<td>\n<p><strong>Statement<\/strong><\/p>\n<\/td>\n<td>\n<p><strong>Reason<\/strong><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p>|CD|= |AC| + |AD|<\/p>\n<\/td>\n<td>\n<p>From figure 3<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p>|CD|= |AC| + |AB|<\/p>\n<\/td>\n<td>\n<p>AB = AD, \u2206ADB is an isosceles triangle<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p>\u2220DBA &lt;\u2220DBC<\/p>\n<\/td>\n<td>\n<p>Since \u2220DBC = \u2220DBA+\u2220ABD<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p>\u2220ADB&lt;\u2220DBC<\/p>\n<\/td>\n<td>\n<p>\u2206ADB is an isosceles triangle and \u2220ADB = \u2220DBA<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p>|BC|&lt;|CD|<\/p>\n<\/td>\n<td>\n<p>The side opposite to the greater angle is a larger<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p>|BC|&lt;|AC| + |AB|<\/p>\n<\/td>\n<td>\n<p>From statements 3 and 4<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>It concludes that the total of two sides of the triangle is greater than the third side.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"examples-of-rd-sharma-chapter-10-class-9-maths-exercise-106-solutions\"><\/span><strong>Examples of RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Ques: Could a triangle have side lengths as 6cm, 7cm, and 5cm?<\/p>\n<p>Solution- If 6cm, 7cm, and 5cm are the sides of a triangle, it satisfies the inequality theorem.<\/p>\n<p>Hence,<\/p>\n<ul>\n<li>6 + 7 &gt; 5 = 13 &gt; 5 = True<\/li>\n<li>7 + 5 &gt; 6 = 12 &gt; 6 = True<\/li>\n<li>6 + 5 &gt; 7 = 11 &gt; 7 = True<\/li>\n<\/ul>\n<p>All three conditions are satisfied. Therefore a triangle could have side lengths as 6cm, 7cm, and 5cm.<\/p>\n<p><strong>Ques- Is it possible to draw a triangle with sides of lengths- 2 cm, 3 cm, and 7 cm?<\/strong><\/p>\n<p><strong>Solution-<\/strong><\/p>\n<p>Lengths of the sides are 2 cm, 3 cm, and 7 cm.<\/p>\n<p>A triangle can be drawn only when the total of any two sides is greater than the third side.<\/p>\n<p>So, let\u2019s check the rule.<\/p>\n<p>2 + 3 \u226f 7 or 2 + 3 &lt; 7<\/p>\n<p>2 + 7 &gt; 3<\/p>\n<p>and 3 + 7 &gt; 2<\/p>\n<p>Here 2 + 3 \u226f 7<\/p>\n<p>So, the triangle does not exist.<\/p>\n<p><a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Know about CBSE Board<\/strong><\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-chapter-10-class-9-maths-exercise-106-solutions\"><\/span>FAQs on RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1680499002042\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"from-where-can-i-download-the-pdf-of-rd-sharma-chapter-10-class-9-maths-exercise-106-solutions\"><\/span>From where can I download the PDF of RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can find the download link from the above blog.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1680499008610\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-much-does-it-cost-to-download-the-pdf-of-rd-sharma-chapter-10-class-9-maths-exercise-106-solutions\"><\/span>How much does it cost to download the PDF of RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can download it for free.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1680499029452\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"can-i-access-the-rd-sharma-chapter-10-class-9-maths-exercise-106-solutions-pdf-offline\"><\/span>Can I access the RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions PDF offline?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Once you have downloaded the PDF online, you can access it offline as well.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions: As we have learned that if two sides of a triangle are equivalent to the angles opposite to them, they are also similar and vice-versa. In this RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions, we will learn about Some Inequality Relations in &#8230; <a title=\"RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-10-class-9-maths-exercise-10-6-solutions\/\" aria-label=\"More on RD Sharma Chapter 10 Class 9 Maths Exercise 10.6 Solutions\">Read more<\/a><\/p>\n","protected":false},"author":241,"featured_media":72862,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2985,2917,73719,73411],"tags":[3081,3086,3085],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72857"}],"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=72857"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72857\/revisions"}],"predecessor-version":[{"id":343472,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72857\/revisions\/343472"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/72862"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=72857"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=72857"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=72857"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}