{"id":5018,"date":"2016-05-19T11:49:00","date_gmt":"2016-05-19T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-11-1\/"},"modified":"2018-06-18T17:26:40","modified_gmt":"2018-06-18T11:56:40","slug":"ncert-solutions-for-class-9-maths-exercise-11-1","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-11-1\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Exercise 11.1"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 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\" style=\"cursor:inherit\">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=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" 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: #999;color:#999\" 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><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-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:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-11-1\/#NCERT_Solutions_for_Class_9_Mathematics_Constructions\" >NCERT Solutions for Class 9 Mathematics Constructions<\/a><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-11-1\/#1_Construct_an_angle_of_at_the_initial_point_of_a_given_ray_and_justify_the_construction\" >1. Construct an angle of  at the initial point of a given ray and justify the construction.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-11-1\/#Justification\" >Justification:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-11-1\/#2_Construct_an_angle_of_at_the_initial_point_of_a_given_ray_and_justify_the_construction\" >2. Construct an angle of  at the initial point of a given ray and justify the construction.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-11-1\/#Justification-2\" >Justification:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-11-1\/#3_Construct_the_angles_of_the_following_measurements\" >3. Construct the angles of the following measurements:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-11-1\/#ii_Steps_of_construction\" >(ii) Steps of construction:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-11-1\/#iii_Steps_of_construction\" >(iii) Steps of construction:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-11-1\/#4_Construct_the_following_angles_and_verify_by_measuring_them_by_a_protactor\" >4. Construct the following angles and verify by measuring them by a protactor:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-11-1\/#Justification-3\" >Justification:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-11-1\/#5_Construct_an_equilateral_triangle_given_its_side_and_justify_the_construction\" >5. Construct an equilateral triangle, given its side and justify the construction.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-11-1\/#Justification-4\" >Justification:<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-11-1\/#NCERT_Solutions_for_Class_9_Maths_Exercise_111\" >NCERT Solutions for Class 9 Maths Exercise 11.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-11-1\/#CBSE_app_for_Class_9\" >CBSE app for Class 9<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 9 Maths Exercise 11.1 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 9 Maths chapter wise NCERT solution for Maths Book for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p style=\"text-align: center;\"><strong>NCERT solutions for Class 9 Maths\u00a0<\/strong><strong>Constructions\u00a0<\/strong><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-09-mathematics-constructions\/1245\/ncert-solutions\/5\/\">Download as PDF<\/a><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg\" alt=\"NCERT Solutions for Class 9 Maths Exercise 11.1\" width=\"170\" height=\"219\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Mathematics_Constructions\"><\/span>NCERT Solutions for Class 9 Mathematics Constructions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"1_Construct_an_angle_of_at_the_initial_point_of_a_given_ray_and_justify_the_construction\"><\/span><strong>1. Construct an angle of <\/strong><img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image001.png\" \/><strong> at the initial point of a given ray and justify the construction.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Steps of construction:<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 445\" style=\"height: 100px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image002.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(a) <\/strong>Draw a ray OA.<\/p>\n<p style=\"text-align: justify;\"><strong>(b)<\/strong> With O as centre and convenient radius, draw an arc LM cutting OA at L.<\/p>\n<p style=\"text-align: justify;\"><strong>(c)<\/strong> Now with L as centre and radius OL, draw an arc cutting the arc LM at P.<\/p>\n<p style=\"text-align: justify;\"><strong>(d)<\/strong> Then taking P as centre and radius OL, draw an arc cutting arc PM at the point Q.<\/p>\n<p style=\"text-align: justify;\"><strong>(e) <\/strong>Join OP to draw the ray OB. Also join O and Q to draw the OC. We observe that:<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOB = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>BOC = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image004.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(f)<\/strong> Now we have to bisect <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>BOC. For this, with P as centre and radius greater than <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image005.png\" \/>PQ draw an arc.<\/p>\n<p style=\"text-align: justify;\"><strong>(g) <\/strong>Now with Q as centre and the same radius as in step 6, draw another arc cutting the arc drawn in step 6 at R.<\/p>\n<p style=\"text-align: justify;\"><strong>(h)<\/strong> Join O and R and draw ray OD.<\/p>\n<p style=\"text-align: justify;\">Then <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOD is the required angle of <img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 448\" style=\"height: 95px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image007.jpg\" \/><\/strong><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Justification\"><\/span><strong>Justification<\/strong>:<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">Join PL, then OL = OP = PL [by construction]\n<p style=\"text-align: justify;\">Therefore <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image008.png\" \/>OQP is an equilateral triangle and <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>POL which is same as <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>BOA is equal to <img decoding=\"async\" style=\"height: 21px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now join QP, then OP = OQ = PQ [ by construction]\n<p style=\"text-align: justify;\">Therefore <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image008.png\" \/>OQP is an equilateral triangle.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image010.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>POQ which is same as <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>BOC is equal to <img decoding=\"async\" style=\"height: 21px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\">By construction OD is bisector of <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>BOC.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image010.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>DOC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>DOB = <img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image011.png\" \/>BOC = <img decoding=\"async\" style=\"height: 41px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image012.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now, <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>DOA = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>BOA + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>DOB<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image013.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>DOA = <img decoding=\"async\" style=\"height: 21px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image014.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image013.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>DOA = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image001.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 11.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_Construct_an_angle_of_at_the_initial_point_of_a_given_ray_and_justify_the_construction\"><\/span><strong>2. Construct an angle of <\/strong><img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image015.png\" \/><strong> at the initial point of a given ray and justify the construction.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Steps of construction<\/strong>:<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 451\" style=\"height: 114px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image016.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(a)<\/strong> Draw a ray OA.<\/p>\n<p style=\"text-align: justify;\"><strong>(b)<\/strong> With O as centre and convenient radius, draw an arc LM cutting OA at L.<\/p>\n<p style=\"text-align: justify;\"><strong>(c)<\/strong> Now with L as centre and radius OL, draw an arc cutting the arc LM at P.<\/p>\n<p style=\"text-align: justify;\"><strong>(d)<\/strong> Then taking P as centre and radius OL, draw an arc cutting arc PM at the point Q.<\/p>\n<p style=\"text-align: justify;\"><strong>(e)<\/strong> Join OP to draw the ray OB. Also join O and Q to draw the OC. We observe that:<img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOB = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>BOC = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image004.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(f)<\/strong> Now we have to bisect <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>BOC. For this, with P as centre and radius greater than <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image005.png\" \/>PQ draw an arc.<\/p>\n<p style=\"text-align: justify;\"><strong>(g)<\/strong> Now with Q as centre and the same radius as in step 6, draw another arc cutting the arc drawn in step 6 at R.<\/p>\n<p style=\"text-align: justify;\"><strong>(h)<\/strong> Join O and R and draw ray OD. Then <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOD is the required angle of <img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong> With L as centre and radius greater than <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image005.png\" \/>LS, draw an arc.<\/p>\n<p style=\"text-align: justify;\"><strong>(j)<\/strong> Now with S as centre and the same radius as in step 2, draw another arc cutting the arc draw in step 2 at T.<\/p>\n<p style=\"text-align: justify;\"><strong>(k)<\/strong> Join O and T and draw ray OE.<\/p>\n<p style=\"text-align: justify;\">Thus OE bisects <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOD and therefore <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOE = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>DOE = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image015.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 454\" style=\"height: 143px; width: 158px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image017.jpg\" \/><\/strong><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Justification-2\"><\/span><strong>Justification<\/strong>:<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">Join LS then <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image008.png\" \/>OLS is isosceles right triangle, right angled at O.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image010.png\" \/> OL = OS<\/p>\n<p style=\"text-align: justify;\">Therefore, O lies on the perpendicular bisector of SL.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image010.png\" \/> SF = FL<\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>OFS = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>OFL [Each <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image001.png\" \/>]\n<p style=\"text-align: justify;\">Now in <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image008.png\" \/>OFS and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image008.png\" \/>OFL,<\/p>\n<p style=\"text-align: justify;\">OF = OF [ Common]\n<p style=\"text-align: justify;\">OS = OL [By construction]\n<p style=\"text-align: justify;\">SF = FL [Proved]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image010.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image008.png\" \/>OFS <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image018.png\" \/>OFL [By SSS rule]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image013.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>SOF = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>LOF [By CPCT]\n<p style=\"text-align: justify;\">Now <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>SOF + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>LOF = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>SOL<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image013.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>SOF + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>LOF = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image001.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image013.png\" \/> 2<img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>LOF = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image001.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image013.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>LOF = <img decoding=\"async\" style=\"height: 41px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image019.png\" \/><\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOE = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image015.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 11.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_Construct_the_angles_of_the_following_measurements\"><\/span><strong>3. Construct the angles of the following measurements:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image020.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image021.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <img decoding=\"async\" style=\"height: 19px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image022.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i) Steps of construction<\/strong>: <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image020.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 457\" style=\"height: 130px; width: 176px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image023.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(a)<\/strong> Draw a ray OA.<\/p>\n<p style=\"text-align: justify;\"><strong>(b)<\/strong> With O as centre and a suitable radius, draw an arc LM that cuts OA at L.<\/p>\n<p style=\"text-align: justify;\"><strong>(c)<\/strong> With L as centre and radius OL, draw an arc to cut LM at N.<\/p>\n<p style=\"text-align: justify;\"><strong>(d)<\/strong> Join O and N draw ray OB. Then <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOB = <img decoding=\"async\" style=\"height: 21px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(e)<\/strong> With L as centre and radius greater than <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image005.png\" \/>LN, draw an arc.<\/p>\n<p style=\"text-align: justify;\"><strong>(f)<\/strong> Now with N as centre and same radius as in step 5, draw another arc cutting the arc drawn in step 5 at P.<\/p>\n<p style=\"text-align: justify;\"><strong>(g)<\/strong> Join O and P and draw ray OC. Thus OC bisects <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOB and therefore <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>BOC = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image020.png\" \/><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"ii_Steps_of_construction\"><\/span><strong>(ii) Steps of construction<\/strong>: <img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image021.png\" \/><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 460\" style=\"height: 115px; width: 161px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image024.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(a) <\/strong>Draw a ray OA.<\/p>\n<p style=\"text-align: justify;\"><strong>(b) <\/strong>With O as centre and convenient radius, draw an arc LM cutting OA at L.<\/p>\n<p style=\"text-align: justify;\"><strong>(c) <\/strong>Now with L as centre and radius OL, draw an arc cutting the arc LM at P.<\/p>\n<p style=\"text-align: justify;\"><strong>(d) <\/strong>Then taking P as centre and radius OL, draw an arc cutting arc PM at the point Q.<\/p>\n<p style=\"text-align: justify;\"><strong>(e) <\/strong>Join OP to draw the ray OB. Also join O and Q to draw the OC. We observe that:<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOB = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>BOC = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image004.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(f) <\/strong>Now we have to bisect <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>BOC. For this, with P as centre and radius greater than <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image005.png\" \/>PQ draw an arc.<\/p>\n<p style=\"text-align: justify;\"><strong>(g) <\/strong>Now with Q as centre and the same radius as in step 6, draw another arc cutting the arc drawn in step 6 at R.<\/p>\n<p style=\"text-align: justify;\"><strong>(h)<\/strong> Join O and R and draw ray OD. Then <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOD is the required angle of <img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong>With L as centre and radius greater than <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image005.png\" \/>LS, draw an arc.<\/p>\n<p style=\"text-align: justify;\"><strong>(j) <\/strong>Now with S as centre and the same radius as in step 2, draw another arc cutting the arc draw in step 2 at T.<\/p>\n<p style=\"text-align: justify;\"><strong>(k)<\/strong> Join O and T and draw ray OE. Thus OE bisects <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOD and therefore <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOE = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>DOE = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image015.png\" \/>.<\/p>\n<p style=\"text-align: justify;\"><strong>(l)<\/strong> Let ray OE intersect the arc of circle at N.<\/p>\n<p style=\"text-align: justify;\"><strong>(m)<\/strong> Now with L as centre and radius greater than <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image005.png\" \/>LN, draw an arc.<\/p>\n<p style=\"text-align: justify;\"><strong>(n)<\/strong> With N as centre and same radius as in above step and draw another arc cutting arc drawn in above step at I.<\/p>\n<p style=\"text-align: justify;\"><strong>(o)<\/strong> Join O and I and draw ray OF. Thus OF bisects <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOE and therefore <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOF = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>EOF = <img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image021.png\" \/>.<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"iii_Steps_of_construction\"><\/span><strong>(iii) Steps of construction: <img decoding=\"async\" style=\"height: 19px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image022.png\" \/> <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 463\" style=\"height: 124px; width: 173px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image025.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(a)<\/strong> Draw a ray OA.<\/p>\n<p style=\"text-align: justify;\"><strong>(b)<\/strong> With O as centre and a suitable radius, draw an arc LM that cuts OA at L.<\/p>\n<p style=\"text-align: justify;\"><strong>(c)<\/strong> With L as centre and radius OL, draw an arc to cut LM at N.<\/p>\n<p style=\"text-align: justify;\"><strong>(d)<\/strong> Join O and N draw ray OB. Then <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOB = <img decoding=\"async\" style=\"height: 21px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(e)<\/strong> With L as centre and radius greater than <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image005.png\" \/>LN, draw an arc.<\/p>\n<p style=\"text-align: justify;\"><strong>(f)<\/strong> Now with N as centre and same radius as in step 5, draw another arc cutting the arc drawn in step 5 at P.<\/p>\n<p style=\"text-align: justify;\"><strong>(g)<\/strong> Join O and P and draw ray OC. Thus OC bisects <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOB and therefore <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>BOC = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image020.png\" \/>.<\/p>\n<p style=\"text-align: justify;\"><strong>(h)<\/strong> Let ray OC intersects the arc of circle at point Q.<\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong> Now with L as centre and radius greater than <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image005.png\" \/>LQ; draw an arc.<\/p>\n<p style=\"text-align: justify;\"><strong>(j)<\/strong> With Q as centre and same radius as in above step, draw another arc cutting the arc shown in above step at R.<\/p>\n<p style=\"text-align: justify;\"><strong>(k)<\/strong> Join O and R and draw ray OS. Thus OS bisects <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOC and therefore <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>COS = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOS = <img decoding=\"async\" style=\"height: 19px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image022.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 11.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_Construct_the_following_angles_and_verify_by_measuring_them_by_a_protactor\"><\/span><strong>4. Construct the following angles and verify by measuring them by a protactor:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image026.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image027.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image028.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i) Step of construction o<\/strong>f <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image026.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 466\" style=\"height: 111px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image029.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">(a) Draw <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>ABE = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image004.png\" \/> and <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>ABF = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image001.png\" \/>. [ Follow the same steps as done in Question 1 and Question 3 (i)]\n<p style=\"text-align: justify;\">(b) Let ray BF intersects the arc of circle at G.<\/p>\n<p style=\"text-align: justify;\">(c) Now with M as centre and radius greater than <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image005.png\" \/>MG draw an arc.<\/p>\n<p style=\"text-align: justify;\">(d) With G as centre and with same radius as in step (c), draw an arc which intersects the previous arc at point H.<\/p>\n<p style=\"text-align: justify;\">(e) Draw a ray BC passing through H which bisects <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>EBF.<\/p>\n<p style=\"text-align: justify;\">Thus <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>ABC = <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image026.png\" \/> is the required angle.<\/p>\n<p style=\"text-align: justify;\"><strong>Justification<\/strong>:<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>EBF = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>ABF \u2013 <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>ABE = <img decoding=\"async\" style=\"height: 21px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image030.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>EBF = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>CBF = <img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image011.png\" \/>EBF = <img decoding=\"async\" style=\"height: 41px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image031.png\" \/> [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image032.png\" \/> BC is the bisector of <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>EBF]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image010.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>ABC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>ABE + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>EBC = <img decoding=\"async\" style=\"height: 19px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image033.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong> (ii) Steps of construction of<\/strong> <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image027.png\" \/><\/p>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 11.1<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 469\" style=\"height: 111px; width: 186px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image034.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\">(a) Draw <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>ABE = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image001.png\" \/> and <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>ABF = <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image035.png\" \/><\/p>\n<p style=\"text-align: justify;\">(b) Let ray BE intersects the arc of circle at M and ray BF intersects the arc of circle N.<\/p>\n<p style=\"text-align: justify;\">(c) With point M as centre and radius greater than <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image005.png\" \/>MN, draw an arc.<\/p>\n<p style=\"text-align: justify;\">(d) With N as centre and with same radius as in step (c), draw another arc which intersects the previous arc at P.<\/p>\n<p style=\"text-align: justify;\">(e) Draw a ray BC passing through P which bisects <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>EBF.<\/p>\n<p style=\"text-align: justify;\">Thus <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>ABC = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image027.png\" \/> is the required angle.<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Justification-3\"><\/span><strong>Justification<\/strong>:<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>EBF = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>ABF \u2013 <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>ABE= <img decoding=\"async\" style=\"height: 21px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image036.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>EBC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>CBF = <img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image011.png\" \/>EBF = <img decoding=\"async\" style=\"height: 41px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image031.png\" \/> [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image032.png\" \/> BC is the bisector of <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>EBF]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image010.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>ABC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>ABE + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>EBC = <img decoding=\"async\" style=\"height: 19px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image037.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong> (iii) Steps of construction of<\/strong> <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image028.png\" \/><\/p>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 11.1<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 472\" style=\"height: 119px; width: 178px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image038.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\">(a) Draw a ray OA.<\/p>\n<p style=\"text-align: justify;\">(b) With O as centre and convenient radius, draw an arc LM (having length more than the semicircle) cutting OA at L.<\/p>\n<p style=\"text-align: justify;\">(c) Now with L as centre and radius = OL; draw an arc cutting the arc LM at P.<\/p>\n<p style=\"text-align: justify;\">(d) Then taking P as centre and radius OL, draw an arc cutting arc PM at Q.<\/p>\n<p style=\"text-align: justify;\">(e) Now bisect <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>POQ by ray OB, we get <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOB = <img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\">(f) Now taking Q as centre and radius OL, draw an arc cutting QM at N.<\/p>\n<p style=\"text-align: justify;\">(g) Join O and N to draw the ray OC.<\/p>\n<p style=\"text-align: justify;\">Thus we get <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOC = <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image039.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image013.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>BOC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOB = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image001.png\" \/><\/p>\n<p style=\"text-align: justify;\">(h) Now bisect <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>BOC by ray OD.<\/p>\n<p style=\"text-align: justify;\">Then <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOD is the required angle of <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image040.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOD = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>AOB + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>BOD = <img decoding=\"async\" style=\"height: 21px; width: 104px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image041.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 11.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_Construct_an_equilateral_triangle_given_its_side_and_justify_the_construction\"><\/span><strong>5. Construct an equilateral triangle, given its side and justify the construction.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Steps of construction<\/strong>:<\/p>\n<p style=\"text-align: justify;\"><strong>(a)<\/strong> Draw a line segment BC of length 6 cm.<\/p>\n<p style=\"text-align: justify;\"><strong>(b)<\/strong> At B draw <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>XBC = <img decoding=\"async\" style=\"height: 21px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(c)<\/strong> Draw perpendicular bisector PQ of line segment BC.<\/p>\n<p style=\"text-align: justify;\"><strong>(d)<\/strong> Let A and D be the points where PQ intersects the ray BX and side BC respectively.<\/p>\n<p style=\"text-align: justify;\"><strong>(e)<\/strong> Join AC.<\/p>\n<p style=\"text-align: justify;\">Thus ABC is the required equilateral triangle.<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Justification-4\"><\/span><strong>Justification<\/strong>:<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 475\" style=\"height: 136px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image042.png\" \/><\/p>\n<p style=\"text-align: justify;\">In right triangle ADB and right triangle ADC,<\/p>\n<p style=\"text-align: justify;\">AD = AD [Common]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>ADB = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>ADC = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image001.png\" \/>[By construction]\n<p style=\"text-align: justify;\">BD = CD [By construction]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image010.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image008.png\" \/>ADB <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image018.png\" \/>ADC [By SAS congruency]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image010.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>B = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>C = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image004.png\" \/> [By CPCT]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image010.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>A = <img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image043.png\" \/> (<img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>B + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>C)<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 29px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image044.png\" \/> = <img decoding=\"async\" style=\"height: 21px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image045.png\" \/> = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image004.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image032.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>A = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>B = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image003.png\" \/>C = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image004.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image010.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch11\/Ex11.1\/image008.png\" \/>ABC is an equilateral triangle.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Maths_Exercise_111\"><\/span>NCERT Solutions for Class 9 Maths Exercise 11.1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions for Class 9 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 9 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 9 Maths have total 15 chapters. 9 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 9 solutions PDF and Maths ncert class 9 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_app_for_Class_9\"><\/span>CBSE app for Class 9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download NCERT Solutions for Class 9 Maths, Computer Science, Home Science,Hindi ,English, Social Science do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 9 Maths Exercise 11.1 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 9 Maths chapter &#8230; <a title=\"NCERT Solutions for Class 9 Maths Exercise 11.1\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-11-1\/\" aria-label=\"More on NCERT Solutions for Class 9 Maths Exercise 11.1\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":-1,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1376,281],"tags":[283,1344,321,1485,216],"class_list":["post-5018","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics-cbse-class-09","category-ncert-solutions","tag-cbse-study-material","tag-class-9","tag-mathematics","tag-maths","tag-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 9 Maths Exercise 11.1 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 9 Maths Exercise 11.1 in PDF format for free download. 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