{"id":126760,"date":"2021-09-15T12:02:59","date_gmt":"2021-09-15T06:32:59","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=126760"},"modified":"2023-12-12T11:11:07","modified_gmt":"2023-12-12T05:41:07","slug":"rd-sharma-class-9-solutions-chapter-12-exercise-12-5","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-9-solutions-chapter-12-exercise-12-5\/","title":{"rendered":"RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5 (Updated for 2024)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-126762\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-9-Solutions-Chapter-12-Exercise-12.5.jpg\" alt=\"\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-9-Solutions-Chapter-12-Exercise-12.5.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-9-Solutions-Chapter-12-Exercise-12.5-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\"><\/p>\n<p><strong>RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5:\u00a0<\/strong>Ace your upcoming Class 9 Maths exam with the <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-9-solutions-for-maths\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Solutions Class 9 Maths<\/a>. Subject matter experts design the solutions of RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5. You can find the download link for <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-12-herons-formula\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Class 9 Solutions Chapter 12<\/a> Exercise 12.5 in this blog. To know more, read the whole blog.\u00a0<\/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-69d7b6c43086f\" 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-69d7b6c43086f\"><\/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-class-9-solutions-chapter-12-exercise-12-5\/#download-rd-sharma-class-9-solutions-chapter-12-exercise-125-pdf\" title=\"Download RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5 PDF\">Download RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5 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-class-9-solutions-chapter-12-exercise-12-5\/#access-answers-of-rd-sharma-class-9-solutions-chapter-12-exercise-125\" title=\"Access answers of RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5\">Access answers of RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-9-solutions-chapter-12-exercise-12-5\/#faqs-on-rd-sharma-class-9-solutions-chapter-12-exercise-125\" title=\"FAQs on RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5\">FAQs on RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-9-solutions-chapter-12-exercise-12-5\/#can-i-access-the-rd-sharma-class-9-solutions-chapter-12-exercise-125-pdf-offline\" title=\"Can I access the RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5\u00a0PDF offline?\">Can I access the RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5\u00a0PDF offline?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-9-solutions-chapter-12-exercise-12-5\/#how-much-does-downloading-the-pdf-of-rd-sharma-class-9-solutions-chapter-12-exercise-125-cost\" title=\"How much does downloading the PDF of RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5 cost?\">How much does downloading the PDF of RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5 cost?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-9-solutions-chapter-12-exercise-12-5\/#from-where-can-i-download-the-pdf-of-rd-sharma-class-9-solutions-chapter-12-exercise-125\" title=\"From where can I download the PDF of RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5?\">From where can I download the PDF of RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-class-9-solutions-chapter-12-exercise-125-pdf\"><\/span><strong>Download RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5 PDF<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-9-Solutions-Chapter-12-Ex-12.5-1.pdf\" target=\"_blank\" rel=\"noopener\">RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5<\/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\/2021\/09\/RD-Sharma-Class-9-Solutions-Chapter-12-Ex-12.5-1.pdf\", \"#example1\");<\/script><\/p>\n<h2><span class=\"ez-toc-section\" id=\"access-answers-of-rd-sharma-class-9-solutions-chapter-12-exercise-125\"><\/span><strong>Access answers of RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Question 1.<br \/>ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles.<br \/>Solution:<br \/>Given: In \u2206ABC, D is the mid-point of BC and DE \u22a5 AB, DF \u22a5 AC, and DE = DF<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1934\/44730127325_804fda0f77_o.png\" alt=\"RD Sharma Class 9 Chapter 12 Heron's Formula\" width=\"268\" height=\"184\" \/><br \/>To Prove: \u2206ABC is an isosceles triangle<br \/>Proof: In the right \u2206BDE and \u2206CDF,<br \/>Side DE = DF<br \/>Hyp. BD = CD<br \/>\u2234 \u2206BDE \u2245 \u2206CDF (RHS axiom)<br \/>\u2234 \u2220B = \u2220C (c.p.c.t.)<br \/>Now in \u2206ABC,<br \/>\u2220B = \u2220C (Prove)<br \/>\u2234 AC = AB (Sides opposite to equal angles)<br \/>\u2234 AABC is an isosceles triangle<\/p>\n<p>Question 2.<br \/>ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that \u2206ABC is an isosceles.<br \/>Solution:<br \/>Given: In \u2206ABC,<br \/>BE \u22a5 AC and CF \u22a5 AB<br \/>BE = CF<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1921\/44730127195_55c1a313e8_o.png\" alt=\"RD Sharma Class 9 Solutions Chapter 12 Heron's Formula\" width=\"283\" height=\"191\" \/><br \/>To prove: AABC is an isosceles triangle<br \/>Proof: In right ABCE and ABCF Side<br \/>BE = CF (Given)<br \/>Hyp. BC = BC (Common)<br \/>\u2234 \u2206BCE \u2245 \u2206BCF (RHS axiom)<br \/>\u2234 \u2220BCE = \u2220CBF (c.p.c.t.)<br \/>\u2234 AB = AC (Sides opposite to equal angles)<br \/>\u2234 \u2206ABC is an isosceles triangle<\/p>\n<p>Question 3.<br \/>If perpendiculars from any point within an angle on its arms are congruent, prove that it lies on the bisector of that angle.<br \/>Solution:<br \/>Given: A point P lies in the angle ABC and PL \u22a5 BA and PM \u22a5 BC and PL = PM. PB is joined<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1966\/43826222590_859785f919_o.png\" alt=\"RD Sharma Solutions Class 9 Chapter 12 Heron's Formula\" width=\"213\" height=\"224\" \/><br \/>To prove: PB is the bisector \u2220ABC,<br \/>Proof: In the right \u2206PLB and \u2206PMB<br \/>Side PL = PM (Given)<br \/>Hyp. PB = PB (Common)<br \/>\u2234 \u2206PLB \u2245 \u2206PMB (RHS axiom)<br \/>\u2234 \u2206PBL = \u2206PBM (c.p.c.t.)<br \/>\u2234 PB is the bisector of \u2220ABC<\/p>\n<p>Question 4.<br \/>In the figure, AD \u22a5 CD and CB \u22a5 CD. If AQ = BP and DP = CQ, prove that \u2220DAQ = \u2220CBP.<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1916\/44730127005_5984cd92a8_o.png\" alt=\"RD Sharma Class 9 PDF Chapter 12 Heron's Formula\" width=\"195\" height=\"176\" \/><br \/>Solution:<br \/>Given: In the figure,<br \/>AD \u22a5 CD and CB \u22a5 CD, AQ = BP and DP = CQ<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1924\/44730126825_a4baef6812_o.png\" alt=\"Heron's Formula Class 9 RD Sharma Solutions\" width=\"211\" height=\"170\" \/><br \/>To prove : \u2220DAQ = \u2220CBP<br \/>Proof : \u2235 DP = CQ<br \/>\u2234 DP + PQ = PQ + QC<br \/>\u21d2 DQ = PC<br \/>Now in the right \u2206ADQ and \u2206BCP<br \/>Side DQ = PC (Proved)<br \/>Hyp. AQ = BP<br \/>\u2234 \u2206ADQ \u2245 \u2206BCP (RHS axiom)<br \/>\u2234 \u2220DAQ = \u2220CBP (c.p.c.t.)<\/p>\n<p>Question 5.<br \/>Which of the following statements are true (T) and which are false (F):<br \/>(i) Sides opposite to equal angles of a triangle may be unequal.<br \/>(ii) Angles opposite to equal sides of a triangle are equal.<br \/>(iii) The measure of each angle of an equilateral triangle is 60\u00b0.<br \/>(iv) If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.<br \/>(v) The bisectors of two equal angles of a triangle are equal.<br \/>(vi) If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.<br \/>(vii) The two altitudes corresponding to two equal sides of a triangle need not be equal.<br \/>(viii)If any two sides of a right triangle are respectively equal to two sides of another right triangle, then the two triangles are congruent.<br \/>(ix) Two right triangles are congruent if the hypotenuse and a side of one triangle are respectively equal to the hypotenuse and a side of the other triangle.<br \/>Solution:<br \/>(i) False: Sides opposite to equal angles of a triangle are equal.<br \/>(ii) True.<br \/>(iii) True.<br \/>(iv) False: The triangle is isosceles.<br \/>(v) True.<br \/>(vi) False: The triangle is an isosceles.<br \/>(vii) False: The altitude is equal.<br \/>(viii) False: If one side and hypotenuse of one right triangle on one side and hypotenuse of the other right triangle are equal, then triangles are congruent.<br \/>(ix) True.<\/p>\n<p>Question 6.<br \/>Fill in the blanks in the following so that each of the following statements is true.<br \/>(i) Sides opposite to equal angles of a triangle are \u2026\u2026.<br \/>(ii) Angle opposite to equal sides of a triangle are \u2026\u2026.<br \/>(iii) In an equilateral triangle all angles are \u2026\u2026.<br \/>(iv) In a \u2206ABC if \u2220A = \u2220C, then AB = \u2026\u2026.<br \/>(v) If altitudes CE and BF of a triangle ABC are equal, then AB = \u2026\u2026..<br \/>(vi) In an isosceles triangle ABC with AB = AC, if BD and CE are its altitudes, then BD is \u2026\u2026\u2026 CE.<br \/>(vii) In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then \u2206ABC \u2245 \u2206\u2026\u2026<br \/>Solution:<br \/>(i) Sides opposite to equal angles of a triangle are equal.<br \/>(ii) Angles opposite to equal sides of a triangle are equal.<br \/>(iii) In an equilateral triangle all angles are equal.<br \/>(iv) In a \u2206ABC, if \u2220A = \u2220C, then AB = BC.<br \/>(v) If altitudes CE and BF of a triangle ABC are equal, then AB = AC.<br \/>(vi) In an isosceles triangle ABC with AB = AC, if BD and CE are its altitudes, then BD is equal to CE.<br \/>(vii) In right triangles ABC and DEF, it hypotenuses AB = EF and side AC = DE, then \u2206ABC \u2245 \u2206EFD.<\/p>\n<p>Question 7.<br \/>ABCD is a square, and X and Y are points on sides AD and BC respectively such that AY = BX. Prove that BY = AX and \u2220BAY = \u2220ABX.<br \/>Solution:<br \/>Given: In square ABCD, X, and Y are points on side AD and BC respectively, and AY = BX<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1971\/44730126665_f4884d6388_o.png\" alt=\"RD Sharma Class 9 Solution Chapter 12 Heron's Formula\" width=\"243\" height=\"225\" \/><br \/>To prove: BY = AX<br \/>\u2220BAY = \u2220ABX<br \/>Proof: In the right \u2206BAX and \u2206ABY<br \/>AB =AB (Common)<br \/>Hyp. BX = AY (Given)<br \/>\u2234 \u2206BAX \u2245 \u2206ABY (RHS axiom)<br \/>\u2234 AX = BY (c.p.c.t.)<br \/>\u2220ABX = \u2220BAY (c.p.c.t.)<br \/>Hence, BY = AX and \u2220BAY = \u2220ABX.<\/p>\n<p>This is the complete blog on RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5. To know more about the <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\">CBSE<\/a> Class 9 Maths exam, ask in the comments.\u00a0<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-class-9-solutions-chapter-12-exercise-125\"><\/span><strong>FAQs on RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5<\/strong><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-1631299839305\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"can-i-access-the-rd-sharma-class-9-solutions-chapter-12-exercise-125-pdf-offline\"><\/span>Can I access the RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5\u00a0PDF 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 id=\"faq-question-1631299864490\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-much-does-downloading-the-pdf-of-rd-sharma-class-9-solutions-chapter-12-exercise-125-cost\"><\/span>How much does downloading the PDF of RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5 cost?<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-1631299890260\" 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-class-9-solutions-chapter-12-exercise-125\"><\/span>From where can I download the PDF of RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5?<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>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5:\u00a0Ace your upcoming Class 9 Maths exam with the RD Sharma Solutions Class 9 Maths. Subject matter experts design the solutions of RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5. You can find the download link for RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5 &#8230; <a title=\"RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5 (Updated for 2024)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-9-solutions-chapter-12-exercise-12-5\/\" aria-label=\"More on RD Sharma Class 9 Solutions Chapter 12 Exercise 12.5 (Updated for 2024)\">Read more<\/a><\/p>\n","protected":false},"author":243,"featured_media":126762,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411],"tags":[3086,4388],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/126760"}],"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\/243"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=126760"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/126760\/revisions"}],"predecessor-version":[{"id":520867,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/126760\/revisions\/520867"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/126762"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=126760"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=126760"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=126760"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}