{"id":5019,"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-5-1\/"},"modified":"2018-06-18T11:58:19","modified_gmt":"2018-06-18T06:28:19","slug":"ncert-solutions-for-class-9-maths-exercise-5-1","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-5-1\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Exercise 5.1"},"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-5-1\/#NCERT_Solutions_for_Class_9_Mathematics_Introduction_to_Euclids_Geometry\" >NCERT Solutions for Class 9 Mathematics\u00a0Introduction to Euclids Geometry<\/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-5-1\/#1_Which_of_the_following_statements_are_true_and_which_are_false_Give_reasons_for_your_answers\" >1. Which of the following statements are true and which are false? Give reasons for your answers.<\/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-5-1\/#ii_False_because_the_given_statement_contradicts_the_postulate_I_of_the_Euclid_that_assures_that_there_is_a_unique_line_that_passes_through_two_distinct_points\" >(ii) False because the given statement contradicts the postulate I of the Euclid that assures that there is a unique line that passes through two distinct points.<\/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-5-1\/#iv_True\" >(iv) True<\/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-5-1\/#v_True\" >(v) True<\/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-5-1\/#2_Give_a_definition_for_each_of_the_following_terms_Are_there_other_terms_that_need_to_be_defined_first_What_are_they_and_how_might_you_define_them\" >2. Give a definition for each of the following terms. Are there other terms that need to be defined first? What are they, and how might you define them?<\/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-5-1\/#iii_Line_segment\" >(iii) Line segment<\/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-5-1\/#3_Consider_the_two_%E2%80%98postulates_given_below\" >3. Consider the two \u2018postulates\u2019 given below:<\/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-5-1\/#4_If_a_point_C_lies_between_two_points_A_and_B_such_that_AC_BC_then_prove_that_Explain_by_drawing_the_figure\" >4. If a point C lies between two points A and B such that AC = BC, then prove that. Explain by drawing the figure.<\/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-5-1\/#5_In_the_above_question_point_C_is_called_a_mid-point_of_line_segment_AB_prove_that_every_line_segment_has_one_and_only_one_mid-point\" >5. In the above question, point C is called a mid-point of line segment AB, prove that every line segment has one and only one mid-point.<\/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-5-1\/#An_axiom_of_the_Euclid_says_that_%E2%80%9CThings_which_are_equal_to_the_same_thing_are_equal_to_one_another%E2%80%9D\" >An axiom of the Euclid says that \u201cThings which are equal to the same thing are equal to one another.\u201d<\/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-5-1\/#6_In_the_following_figure_if_AC_BD_then_prove_that_AB_CD\" >6. In the following figure, if AC = BD, then prove that AB = CD.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-5-1\/#7_Why_is_axiom_5_in_the_list_of_Euclids_axioms_considered_as_a_%E2%80%98universal_truth_Note_that_the_question_if_not_about_fifth_postulate\" >7. Why is axiom 5, in the list of Euclid\u2019s axioms, considered as a \u2018universal truth\u2019? (Note that the question if not about fifth postulate)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-5-1\/#Mathematical_proof\" >Mathematical proof:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-5-1\/#Universal_proof\" >Universal proof:<\/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-16\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-5-1\/#NCERT_Solutions_for_Class_9_Maths_Exercise_51\" >NCERT Solutions for Class 9 Maths Exercise 5.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-5-1\/#CBSE_app_for_Class_9\" >CBSE app for Class 9<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 9 Maths Exercise 5.1 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>Introduction to Euclids Geometry\u00a0<\/strong><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-09-mathematics-introduction-to-euclids-geometry\/1239\/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 5.1\" width=\"184\" height=\"237\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Mathematics_Introduction_to_Euclids_Geometry\"><\/span>NCERT Solutions for Class 9 Mathematics\u00a0Introduction to Euclids Geometry<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"1_Which_of_the_following_statements_are_true_and_which_are_false_Give_reasons_for_your_answers\"><\/span><strong>1. Which of the following statements are true and which are false? Give reasons for your answers.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) Only one line can pass through a single point.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) There are infinite number of lines which pass through two distinct points.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) A terminated line can be produced indefinitely on both the sides.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) If two circles are equal, then their radii are equal.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(v) In Fig. 5.9, if AB = PQ and PQ = XY, then AB = XY<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 7\" style=\"height: 61px; width: 345px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image001.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans.(i) False<\/strong><\/p>\n<p style=\"text-align: justify;\">Correct statement: Infinite many lines can pass through a single point.<\/p>\n<p style=\"text-align: justify;\">This is self-evident and can be seen visually by the student given below:<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 10\" style=\"height: 112px; width: 137px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image002.jpg\" \/><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"ii_False_because_the_given_statement_contradicts_the_postulate_I_of_the_Euclid_that_assures_that_there_is_a_unique_line_that_passes_through_two_distinct_points\"><\/span><strong>(ii) False<\/strong> because the given statement contradicts the postulate I of the Euclid that assures that there is a unique line that passes through two distinct points.<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 13\" style=\"height: 38px; width: 228px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image003.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">Through two points P and Q a unique line can be drawn.<\/p>\n<p style=\"text-align: justify;\"><strong>(iii) True <\/strong><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 16\" style=\"height: 31px; width: 233px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image004.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">Reason:<\/p>\n<p style=\"text-align: justify;\">We need to consider Euclid\u2019s Postulate 2: \u201cA terminated line can be produced indefinitely.\u201d<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"iv_True\"><\/span><strong>(iv) True<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">Reason:<\/p>\n<p style=\"text-align: justify;\">Let us consider two circles with same radii.<\/p>\n<p style=\"text-align: justify;\">We can conclude that, when we make the two circles overlap with each other, we will get a superimposed figure of the two circles.<\/p>\n<p style=\"text-align: justify;\">Therefore, we can conclude that the radii of both the circles will also coincide and will be same.<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"v_True\"><\/span><strong>(v) True<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">Reason:<\/p>\n<p style=\"text-align: justify;\">We are given that AB = PQ and PQ = XY.<\/p>\n<p style=\"text-align: justify;\">We need to consider the axiom: \u201cGiven two distinct points, there is a unique line that passes through them.\u201d<\/p>\n<p style=\"text-align: justify;\">Therefore, we can conclude that AB, PQ and XY are the lines with same dimensions, and hence if AB = PQ and PQ = XY, then AB = XY.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 5.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_Give_a_definition_for_each_of_the_following_terms_Are_there_other_terms_that_need_to_be_defined_first_What_are_they_and_how_might_you_define_them\"><\/span><strong>2. Give a definition for each of the following terms. Are there other terms that need to be defined first? What are they, and how might you define them?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) parallel lines <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) perpendicular lines <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) line segment<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) radius of a circle <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(v) square<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i) <\/strong>Parallel lines<\/p>\n<p style=\"text-align: justify;\">Two lines are said to be parallel, when the perpendicular distance between these lines is always constant or we can say that the lines that never intersect each other are called as parallel lines.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 1\" style=\"height: 106px; width: 168px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image005.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">We need to define line first, in order to define parallel lines.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>Perpendicular lines<\/p>\n<p style=\"text-align: justify;\">Two lines are said to be perpendicular lines, when angle between these two lines is<img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image006.png\" \/>.<\/p>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 5.1<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 6\" style=\"height: 130px; width: 192px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image007.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">We need to define line and angle, in order to define perpendicular lines.<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"iii_Line_segment\"><\/span><strong>(iii) <\/strong>Line segment<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">A line of a fixed dimension between two given points is called as a line segment.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 9\" style=\"height: 61px; width: 293px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image008.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">We need to define line and point, in order to define a line segment.<\/p>\n<p style=\"text-align: justify;\"><strong>(iv) <\/strong>Radius of a circle<\/p>\n<p style=\"text-align: justify;\">The distance of any point lying on the boundary of a circle from the center of the circle is called as radius of a circle.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 12\" style=\"height: 170px; width: 203px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image009.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">We need to define circle and center of a circle, in order to define radius of a circle.<\/p>\n<p style=\"text-align: justify;\"><strong>(v) <\/strong>Square<\/p>\n<p style=\"text-align: justify;\">A quadrilateral with all four sides equal and all four angles of<img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image006.png\" \/> is called as a square.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 17\" style=\"height: 216px; width: 255px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image010.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">We need to define quadrilateral and angle, in order to define a square.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 5.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_Consider_the_two_%E2%80%98postulates_given_below\"><\/span><strong>3. Consider the two \u2018postulates\u2019 given below:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) Given any two distinct points A and B, there exists a third point C, which is between A and B.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) There exists at least three points that are not on the same line.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid\u2019s postulates? Explain.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We are given with following two postulates<\/p>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong>Given any two distinct points A and B, there exists a third point C, which is between A and B.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>There exists at least three points that are not on the same line.<\/p>\n<p style=\"text-align: justify;\">The undefined terms in the given postulates are point and line.<\/p>\n<p style=\"text-align: justify;\">The two given postulates are consistent, as they do not refer to similar situations and they refer to two different situations.<\/p>\n<p style=\"text-align: justify;\">We can also conclude that, it is impossible to derive at any conclusion or any statement that contradicts any well-known axiom and postulate.<\/p>\n<p style=\"text-align: justify;\">The two given postulates do not follow from the postulates given by Euclid.<\/p>\n<p style=\"text-align: justify;\">The two given postulates can be observed following from the axiom, \u201cGiven two distinct points, there is a unique line that passes through them\u201d.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 5.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_If_a_point_C_lies_between_two_points_A_and_B_such_that_AC_BC_then_prove_that_Explain_by_drawing_the_figure\"><\/span><strong>4. If a point C lies between two points A and B such that AC = BC, then prove that<img decoding=\"async\" style=\"height: 41px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image011.png\" \/>. Explain by drawing the figure.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We are given that a point <em>C<\/em> lies between two points <em>B<\/em> and <em>C<\/em>, such that <em>AC<\/em> = <em>BC<\/em>.<\/p>\n<p style=\"text-align: justify;\">We need to prove that<img decoding=\"async\" style=\"height: 41px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image011.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">Let us consider the given below figure.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 23\" style=\"height: 36px; width: 246px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image012.png\" \/><\/p>\n<p style=\"text-align: justify;\">We are given that <em>AC<\/em> = <em>BC<\/em>.\u2026(<em>i<\/em>)<\/p>\n<p style=\"text-align: justify;\">An axiom of the Euclid says that \u201cIf equals are added to equals, the wholes are equal.\u201d<\/p>\n<p style=\"text-align: justify;\">Let us add <em>AC<\/em> to both sides of equation (<em>i<\/em>).<\/p>\n<p style=\"text-align: justify;\"><em>AC <\/em>+ <em>AC<\/em> = <em>BC<\/em> + <em>AC<\/em>.<\/p>\n<p style=\"text-align: justify;\">An axiom of the Euclid says that \u201cThings which coincide with one another are equal to one another.\u201d<\/p>\n<p style=\"text-align: justify;\">We can conclude that <em>BC<\/em> + <em>AC<\/em> coincide with <em>AB<\/em>, or<\/p>\n<p style=\"text-align: justify;\"><em>AB<\/em> = <em>BC<\/em> + <em>AC<\/em>.\u2026(<em>ii<\/em>)<\/p>\n<p style=\"text-align: justify;\">An axiom of the Euclid says that \u201cThings which are equal to the same thing are equal to one another.\u201d<\/p>\n<p style=\"text-align: justify;\">From equations (<em>i<\/em>) and (<em>ii<\/em>), we can conclude that<\/p>\n<p style=\"text-align: justify;\"><em>AC<\/em> + <em>AC<\/em> = <em>AB<\/em>, or<em>2AC<\/em> = <em>AB<\/em>.<\/p>\n<p style=\"text-align: justify;\">An axiom of the Euclid says that \u201cThings which are halves of the same things are equal to one another.\u201d<\/p>\n<p style=\"text-align: justify;\">Therefore, we can conclude that<img decoding=\"async\" style=\"height: 41px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image011.png\" \/>.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 5.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_In_the_above_question_point_C_is_called_a_mid-point_of_line_segment_AB_prove_that_every_line_segment_has_one_and_only_one_mid-point\"><\/span><strong>5. In the above question, point C is called a mid-point of line segment AB, prove that every line segment has one and only one mid-point.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We need to prove that every line segment has one and only one mid-point.<\/p>\n<p style=\"text-align: justify;\">Let us consider the given below line segment <em>AB<\/em> and assume that <em>C<\/em> and <em>D<\/em> are the mid-points of the line segment <em>AB<\/em>.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 22\" style=\"height: 41px; width: 254px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image013.png\" \/><\/p>\n<p style=\"text-align: justify;\">If <em>C<\/em> is the mid-point of line segment <em>AB<\/em>, then<\/p>\n<p style=\"text-align: justify;\"><em>AC <\/em>= <em>CB<\/em>.<\/p>\n<p style=\"text-align: justify;\">An axiom of the Euclid says that \u201cIf equals are added to equals, the wholes are equal.\u201d<\/p>\n<p style=\"text-align: justify;\"><em>AC <\/em>+ <em>AC <\/em>= <em>CB<\/em> + <em>AC<\/em>.(i)<\/p>\n<p style=\"text-align: justify;\">From the figure, we can conclude that <em>CB<\/em> + <em>AC<\/em> will coincide with <em>AB<\/em>.<\/p>\n<p style=\"text-align: justify;\">An axiom of the Euclid says that \u201cThings which coincide with one another are equal to one another.\u201d<\/p>\n<p style=\"text-align: justify;\"><em>AC <\/em>+ <em>AC <\/em>= <em>AB<\/em>.(ii)<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"An_axiom_of_the_Euclid_says_that_%E2%80%9CThings_which_are_equal_to_the_same_thing_are_equal_to_one_another%E2%80%9D\"><\/span>An axiom of the Euclid says that \u201cThings which are equal to the same thing are equal to one another.\u201d<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">Let us compare equations (i) and (ii), to get<\/p>\n<p style=\"text-align: justify;\"><em>AC<\/em> + <em>AC<\/em> = <em>AB<\/em>, or2<em>AC<\/em> = <em>AB<\/em>.(iii)<\/p>\n<p style=\"text-align: justify;\">If <em>D<\/em> is the mid-point of line segment <em>AB<\/em>, then<\/p>\n<p style=\"text-align: justify;\"><em>AD <\/em>= <em>DB<\/em>.<\/p>\n<p style=\"text-align: justify;\">An axiom of the Euclid says that \u201cIf equals are added to equals, the wholes are equal.\u201d<\/p>\n<p style=\"text-align: justify;\"><em>AD <\/em>+ <em>AD <\/em>= <em>DB<\/em> + <em>AD<\/em>.(iv)<\/p>\n<p style=\"text-align: justify;\">From the figure, we can conclude that <em>DB<\/em> + <em>AD<\/em> will coincide with <em>AB<\/em>.<\/p>\n<p style=\"text-align: justify;\">An axiom of the Euclid says that \u201cThings which coincide with one another are equal to one another.\u201d<\/p>\n<p style=\"text-align: justify;\"><em>AD <\/em>+ <em>AD <\/em>= <em>AB<\/em>.(v)<\/p>\n<p style=\"text-align: justify;\">An axiom of the Euclid says that \u201cThings which are equal to the same thing are equal to one another.\u201d<\/p>\n<p style=\"text-align: justify;\">Let us compare equations (iv) and (v), to get<\/p>\n<p style=\"text-align: justify;\"><em>AD<\/em> + <em>AD<\/em> = <em>AB<\/em>, or<\/p>\n<p style=\"text-align: justify;\">2<em>AD<\/em> = <em>AB<\/em>.(vi)<\/p>\n<p style=\"text-align: justify;\">An axiom of the Euclid says that \u201cThings which are equal to the same thing are equal to one another.\u201d<\/p>\n<p style=\"text-align: justify;\">Let us compare equations (iii) and (vi), to get<\/p>\n<p style=\"text-align: justify;\"><em>2AC<\/em> = <em>2AD<\/em>.<\/p>\n<p style=\"text-align: justify;\">An axiom of the Euclid says that \u201cThings which are halves of the same things are equal to one another.\u201d<\/p>\n<p style=\"text-align: justify;\"><em>AC<\/em> = <em>AD<\/em>.<\/p>\n<p style=\"text-align: justify;\">Therefore, we can conclude that the assumption that we made previously is false and a line segment has one and only one mid-point.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 5.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_In_the_following_figure_if_AC_BD_then_prove_that_AB_CD\"><\/span><strong>6. In the following figure, if AC = BD, then prove that AB = CD.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 48px; width: 182px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image014.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We are given that <em>AC<\/em> = <em>BD<\/em>.<\/p>\n<p style=\"text-align: justify;\">We need to prove that <em>AB<\/em> = <em>CD<\/em> in the figure given below.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 24\" style=\"height: 64px; width: 243px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image015.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">From the figure, we can conclude that<\/p>\n<p style=\"text-align: justify;\"><em>AC<\/em> = <em>AB<\/em> + <em>BC<\/em>, and<\/p>\n<p style=\"text-align: justify;\"><em>BD<\/em> = <em>CD<\/em> + <em>BC<\/em>.<\/p>\n<p style=\"text-align: justify;\">An axiom of the Euclid says that \u201cThings which are equal to the same thing are equal to one another.\u201d<\/p>\n<p style=\"text-align: justify;\"><em>AB<\/em> + <em>BC <\/em>= <em>CD<\/em> + <em>BC<\/em>. (i)<\/p>\n<p style=\"text-align: justify;\">An axiom of the Euclid says that \u201cwhen equals are subtracted from equals, the remainders are also equal.\u201d<\/p>\n<p style=\"text-align: justify;\">We need to subtract <em>BC<\/em> from equation (i), to get<\/p>\n<p style=\"text-align: justify;\"><em>AB<\/em> + <em>BC<\/em> &#8211; <em>BC <\/em>= <em>CD<\/em> + <em>BC<\/em> &#8211; <em>BC<\/em><\/p>\n<p style=\"text-align: justify;\"><em>AB<\/em> = <em>CD<\/em>.<\/p>\n<p style=\"text-align: justify;\">Therefore, we can conclude that the desired result is proved.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 5.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_Why_is_axiom_5_in_the_list_of_Euclids_axioms_considered_as_a_%E2%80%98universal_truth_Note_that_the_question_if_not_about_fifth_postulate\"><\/span><strong>7. Why is axiom 5, in the list of Euclid\u2019s axioms, considered as a \u2018universal truth\u2019? (Note that the question if not about fifth postulate)<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We need to prove that Euclid\u2019s fifth axiom is considered as a universal truth.<\/p>\n<p style=\"text-align: justify;\">Euclid\u2019s fifth axiom states that \u201cthe whole is greater than the part.\u201d<\/p>\n<p style=\"text-align: justify;\">The above given axiom is a universal truth. We can apply the fifth axiom not only mathematically but also universally in daily life.<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Mathematical_proof\"><\/span><strong>Mathematical proof:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">Let us consider a quantity <em>z<\/em>, which has different parts as <em>a<\/em>, <em>b<\/em>, <em>x<\/em> and <em>y<\/em>.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch05\/Ex5.1\/image016.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">Therefore, we can conclude that <em>z<\/em> will always be greater than its corresponding parts <em>a<\/em>, <em>b<\/em>, <em>x<\/em> and <em>y<\/em>.<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Universal_proof\"><\/span><strong>Universal proof:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">We know that Mumbai is located in Maharashtra and Maharashtra is located in India.<\/p>\n<p style=\"text-align: justify;\">In other words, we can conclude that Mumbai is a part of Maharashtra and Maharashtra is a part of India.<\/p>\n<p style=\"text-align: justify;\">Therefore, we can conclude that whole India will be greater than Mumbai or Maharashtra or both.<\/p>\n<p style=\"text-align: justify;\">Therefore, we can conclude that Euclid\u2019s fifth axiom is considered as a \u2018Universal truth\u2019.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Maths_Exercise_51\"><\/span>NCERT Solutions for Class 9 Maths Exercise 5.1<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 5.1 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. 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