{"id":122706,"date":"2022-02-20T11:17:39","date_gmt":"2022-02-20T05:47:39","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=122706"},"modified":"2024-10-21T14:10:09","modified_gmt":"2024-10-21T08:40:09","slug":"ncert-exemplar-solutions-for-class-9-maths-chapter-5-introduction-to-euclids-geometry-infinity-learn","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-5-introduction-to-euclids-geometry\/","title":{"rendered":"NCERT Exemplar Solutions for Class 9 Maths Chapter 5 &#8211; Introduction to Euclid\u2019s Geometry"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><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><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-5-introduction-to-euclids-geometry\/#Download_the_PDF_of_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_5_Introduction_to_Euclids_Geometry\" title=\"Download the PDF of NCERT Exemplar Solutions for Class 9 Maths Chapter 5 Introduction to Euclid\u2019s Geometry\">Download the PDF of NCERT Exemplar Solutions for Class 9 Maths Chapter 5 Introduction to Euclid\u2019s Geometry<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-2\" 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href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-5-introduction-to-euclids-geometry\/#More_Resources_for_Class_9\" title=\"More Resources for Class 9\">More Resources for Class 9<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-5-introduction-to-euclids-geometry\/#NCERT_Exemplar_Class_9_Maths_Chapter_5_Exercise_52\" title=\"NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.2\">NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-5-introduction-to-euclids-geometry\/#NCERT_Exemplar_Class_9_Maths_Chapter_5_Exercise_53\" title=\"NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.3\">NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-5-introduction-to-euclids-geometry\/#NCERT_Exemplar_Class_9_Maths_Chapter_5_Exercise_54\" title=\"NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.4\">NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.4<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-5-introduction-to-euclids-geometry\/#Real-World_Applications_of_Euclids_Geometry\" title=\"Real-World Applications of Euclid\u2019s Geometry\">Real-World Applications of Euclid\u2019s Geometry<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-5-introduction-to-euclids-geometry\/#Why_Study_Euclids_Geometry_with_NCERT_Exemplar_Solutions\" title=\"Why Study Euclid\u2019s Geometry with NCERT Exemplar Solutions?\">Why Study Euclid\u2019s Geometry with NCERT Exemplar Solutions?<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-5-introduction-to-euclids-geometry\/#Introduction_to_Euclids_Geometry_FAQs\" title=\"Introduction to Euclids Geometry FAQ&#8217;s\">Introduction to Euclids Geometry FAQ&#8217;s<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-5-introduction-to-euclids-geometry\/#Is_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_5_suitable_for_CBSE_students\" title=\"Is NCERT Exemplar Solutions for Class 9 Maths Chapter 5 suitable for CBSE students?\">Is NCERT Exemplar Solutions for Class 9 Maths Chapter 5 suitable for CBSE students?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-5-introduction-to-euclids-geometry\/#Where_can_I_download_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_5\" title=\"Where can I download NCERT Exemplar Solutions for Class 9 Maths Chapter 5?\">Where can I download NCERT Exemplar Solutions for Class 9 Maths Chapter 5?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-5-introduction-to-euclids-geometry\/#What_is_the_meaning_of_Euclidean_geometry_according_to_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_5\" title=\"What is the meaning of Euclidean geometry according to NCERT Exemplar Solutions for Class 9 Maths Chapter 5?\">What is the meaning of Euclidean geometry according to NCERT Exemplar Solutions for Class 9 Maths Chapter 5?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><strong>Introduction to Euclid\u2019s Geometry<\/strong> is a crucial chapter for students preparing for Class 9 Maths. It introduces the foundational concepts of geometry through the work of the ancient Greek mathematician <strong>Euclid<\/strong>, which is essential for building a strong base in understanding geometric theorems and axioms.<\/p>\n<p><strong>This chapter covers:<\/strong><\/p>\n<ul>\n<li><strong>Basic Definitions of Geometry<\/strong>: Learn about points, lines, and planes, and how these basic elements form the foundation of all geometric studies.<\/li>\n<li><strong>Euclid\u2019s Axioms and Postulates<\/strong>: Understand Euclid\u2019s approach to geometry, which consists of assumptions (axioms) and logical deductions (postulates) that help form geometric theorems.<\/li>\n<\/ul>\n<p>By going through the <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/\"><strong>NCERT Exemplar Solutions<\/strong><\/a> provided here, students can gain a better understanding of the basic structure and logic of geometry, which will be beneficial not only for their exams but also for further studies in Mathematics.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Download_the_PDF_of_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_5_Introduction_to_Euclids_Geometry\"><\/span>Download the PDF of NCERT Exemplar Solutions for Class 9 Maths Chapter 5 Introduction to Euclid\u2019s Geometry<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Download detailed step-by-step solutions PDF for all the exercises in NCERT Class 9 Maths Chapter 5: Introduction to Euclid\u2019s Geometry. These solutions are designed to help students understand the concepts clearly and solve problems with confidence.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Key_Concepts_Covered\"><\/span><strong>Key Concepts Covered:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li><strong>Definition of Point and Line<\/strong>: Explanation of the most fundamental terms in geometry.<\/li>\n<li><strong>Euclid\u2019s Five Postulates<\/strong>: Understanding the basis of Euclid\u2019s geometry, from the first postulate (a straight line may be drawn from any point to any other point) to the fifth postulate (the famous parallel postulate).<\/li>\n<li><strong>Proofs and Theorems<\/strong>: Logical deductions from the postulates are used to prove basic theorems in geometry.<\/li>\n<\/ul>\n<p>By practicing these exemplar problems, students will be able to master the logic and reasoning skills required to excel in geometry.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Access_Answers_to_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_5_Introduction_to_Euclids_Geometry\"><\/span>Access Answers to NCERT Exemplar Solutions for Class 9 Maths Chapter 5 Introduction to Euclid\u2019s Geometry<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Question 1. The three steps from solids to points are:<\/strong><\/p>\n<p>(A) Solids-surfaces-lines-points<\/p>\n<p>(B) Solids-lines-surfaces-points<\/p>\n<p>(C) Lines-points-sufaces-solids<\/p>\n<p>(D) Lines-surfaces-points-solids<\/p>\n<p><strong>Solution: <\/strong>(A): The three steps from solids to points are solids-surfaces-lines-points.<\/p>\n<p><strong>Question 2. The number of dimensions, a solid has:<\/strong><\/p>\n<p>(A) 1<\/p>\n<p>(B) 2<\/p>\n<p>(C) 3<\/p>\n<p>(D) 0<\/p>\n<p><strong>Solution: <\/strong>(C): A solid e.g., Cuboid has shape, size, and position. So, solid has three dimensions.<\/p>\n<div class=\"card\" style=\"text-align: center;\"><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/online-mock-tests?utm_source=surge&amp;utm_medium=interlinking\"><br \/>\n<img loading=\"lazy\" class=\" lazyloaded\" style=\"width: 100%; border-radius: 10px;\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/cvc.png\" alt=\"online mock test\" width=\"1201\" height=\"636\" data-src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/cvc.png\" \/><\/a><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/online-mock-tests?utm_source=surge&amp;utm_medium=interlinking\"><button><strong>Online Mock Test<\/strong><\/button><\/a><\/p>\n<div style=\"text-align: center;\">Boost Your Preparation With Our Free Online Mock Tests For IIT-JEE, NEET And CBSE Exams<\/div>\n<\/div>\n<p><strong>Question 3. The number of dimensions, a surface has:<\/strong><\/p>\n<p>(A) 1<\/p>\n<p>(B) 2<\/p>\n<p>(C) 3<\/p>\n<p>(D) 0<\/p>\n<p><strong>Solution: <\/strong>(B): Boundaries of a solid are called surfaces. A surface (plane) has only length and breadth. So, it has two dimensions.<\/p>\n<p><strong>Question 4. The number of dimension, a point has<\/strong><\/p>\n<p>(A) 0<\/p>\n<p>(B) 1<\/p>\n<p>(C) 2<\/p>\n<p>(D) 3<\/p>\n<p><strong>Solution: <\/strong>(A): A point is that which has no part i. e., no length, no breadth and no height. So, it has no dimension.<\/p>\n<p><strong>Question 5. Euclid divided his famous treatise \u201cThe Elements\u201d into<\/strong><\/p>\n<p>(A) 13 chapters<\/p>\n<p>(B) 12 chapters<\/p>\n<p>(C) 11 chapters<\/p>\n<p>(D) 9 chapters<\/p>\n<p><strong>Solution: <\/strong>(A)<\/p>\n<p>Euclid divided his famous treatise \u2018The Elements\u201d into 13 chapters.<\/p>\n<p><strong>Question 6. The total number of propositions in the Elements are<\/strong><\/p>\n<p>(A) 465<\/p>\n<p>(B) 460<\/p>\n<p>(C) 13<\/p>\n<p>(D) 55<\/p>\n<p><strong>Solution: <\/strong>(A)<\/p>\n<p>The statements that can be proved are called propositions or theorems. Euclid deduced 465 propositions in a logical chain using his axioms, postulates, definitions and theorems.<\/p>\n<p><strong>Question 7. Boundaries of solids are:<\/strong><\/p>\n<p>(A) surfaces<\/p>\n<p>(B) curves<\/p>\n<p>(C) lines<\/p>\n<p>(D) points<\/p>\n<p><strong>Solution: <\/strong>(A): Boundaries of solids are surfaces.<\/p>\n<p><strong>Question 8. Boundaries of surfaces are:<\/strong><\/p>\n<p>(A) surfaces<\/p>\n<p>(B) curves<\/p>\n<p>(C) lines<\/p>\n<p>(D) points<\/p>\n<p><strong>Solution: <\/strong>(B) : The boundaries of surfaces are curves.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"More_Resources_for_Class_9\"><\/span>More Resources for Class 9<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/\"><strong>NCERT Exemplar for Class 9<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/science\/\"><strong>NCERT Exemplar for Class 9 Science<\/strong><\/a><\/li>\n<\/ul>\n<p><strong>Question 9. <\/strong>In Indus Valley Civilization (about 3000 B.C.), the bricks used for construction work were having dimensions in the ratio<\/p>\n<p>(A) 1 : 3 : 4<\/p>\n<p>(B) 4 : 2 : 1<\/p>\n<p>(C) 4 : 4 : 1<\/p>\n<p>(D) 4 : 3 : 2<\/p>\n<p><strong>Solution: <\/strong>(B)<\/p>\n<p>In Indus Valley Civilization, the bricks used for construction work were having dimensions in the ratio length : breadth : thickness = 4 : 2 : 1.<\/p>\n<p><strong>Question 10. A pyramid is a solid figure, the base of which is<\/strong><\/p>\n<p>(A) only a triangle<\/p>\n<p>(B) only a square<\/p>\n<p>(C) only a rectangle<\/p>\n<p>(D) any polygon<\/p>\n<p><strong>Solution: <\/strong>(D)<\/p>\n<p>A pyramid is a solid figure, the base of which is a triangle or square or some other polygon.<\/p>\n<p><strong>Question 11. The side faces of a pyramid are<\/strong><\/p>\n<p>(A) Triangles<\/p>\n<p>(B) Squares<\/p>\n<p>(C) Polygons<\/p>\n<p>(D) Trapeziums<\/p>\n<p><strong>Solution: <\/strong>(A)<\/p>\n<p>The side faces of a pyramid are always triangles.<\/p>\n<p><strong>Question 12. It is known that, if x + y = 10, then x + y + z = 10 + z. The Euclid\u2019s axiom that illustrates this statement is:<\/strong><\/p>\n<p>(A) First Axiom<\/p>\n<p>(B) Second Axiom<\/p>\n<p>(C) Third Axiom<\/p>\n<p>(D) Fourth Axiom<\/p>\n<p><strong>Solution: <\/strong>(B)<\/p>\n<p>The Euclid\u2019s axiom that illustrates the given statement is second axiom. According to this, if equals are added to equals, the wholes are equal.<\/p>\n<p><strong>Question 13. In ancient India, the shapes of altars used for household rituals were:<\/strong><\/p>\n<p>(A) Squares and circles<\/p>\n<p>(B) Triangles and rectangles<\/p>\n<p>(C) Trapeziums and pyramids<\/p>\n<p>(D) Rectangles and squares<\/p>\n<p><strong>Solution: <\/strong>(A)<\/p>\n<p>In ancient India, squares and circular altars were used for household rituals.<\/p>\n<p><strong>Question 14. <\/strong>The number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is:<\/p>\n<p>(A) Seven<\/p>\n<p>(B) Eight<\/p>\n<p>(C) Nine<\/p>\n<p>(D) Eleven<\/p>\n<p><strong>Solution: <\/strong>(C)<\/p>\n<p>The Sriyantra (in the Atharvaveda) consists of nine interwoven isosceles triangles.<\/p>\n<p><strong>Question 15. <\/strong>Greek\u2019s emphasised on:<\/p>\n<p>(A) Inductive reasoning<\/p>\n<p>(B) Deductive reasoning<\/p>\n<p>(C) Both (A) and (B)<\/p>\n<p>(D) Practical use of geometry<\/p>\n<p><strong>Solution: <\/strong>(B)<\/p>\n<p>Greek\u2019s emphasised on deductive reasoning.<\/p>\n<p><strong>Question 16. In ancient India, altars with combination of shapes like rectangles, triangles and trapeziums were used for<\/strong><\/p>\n<p>(A) Public worship<\/p>\n<p>(B) Household rituals<\/p>\n<p>(C) Both (A) and (B)<\/p>\n<p>(D) None of A, B, C<\/p>\n<p><strong>Solution: <\/strong>(A)<\/p>\n<p>In ancient India altars whose shapes were combinations of rectangles, triangles and trapeziums were used for public worship.<\/p>\n<p><strong>Question 17. Euclid belongs to the country:<\/strong><\/p>\n<p>(A) Babylonia<\/p>\n<p>(B) Egypt<\/p>\n<p>(C) Greece<\/p>\n<p>(D) India<\/p>\n<p><strong>Solution: <\/strong>(C)<\/p>\n<p>Euclid belongs to the country Greece.<\/p>\n<p><strong>Question 18. Thales belongs to the country:<\/strong><\/p>\n<p>(A) Babylonia<\/p>\n<p>(B) Egypt<\/p>\n<p>(C) Greece<\/p>\n<p>(D) Rome<\/p>\n<p><strong>Solution: <\/strong>(C)<\/p>\n<p>Thales belongs to the country Greece.<\/p>\n<div class=\"card\" style=\"text-align: center;\"><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/one-stop-solutions-for-school-prep?utm_source=surge&amp;utm_medium=interlinking\"><br \/>\n<img loading=\"lazy\" class=\" lazyloaded\" style=\"width: 100%; border-radius: 10px;\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/one-stop-solution-for-school-exam.jpg\" alt=\"one-stop-solutions school exam\" width=\"1201\" height=\"636\" data-src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/one-stop-solution-for-school-exam.jpg\" \/><\/a><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/one-stop-solutions-for-school-prep?utm_source=surge&amp;utm_medium=interlinking\"><button><strong>One Stop Solutions for School Exam Preparation<\/strong><\/button><\/a><\/p>\n<div style=\"text-align: center;\">Boost your school preparation with our comprehensive guide for CBSE, ICSE, and State Board exams. Get all the resources you need in one place and excel in your academic journey. Discover the ultimate one-stop solution at Infinity Learn today!<\/div>\n<\/div>\n<p><strong>Question 19. Pythagoras was a student of:<\/strong><\/p>\n<p>(A) Thales<\/p>\n<p>(B) Euclid<\/p>\n<p>(C) Both (A) and (B)<\/p>\n<p>(D) Archimedes<\/p>\n<p><strong>Solution: <\/strong>(A)<\/p>\n<p>Pythagoras was a student of Thales.<\/p>\n<p><strong>Question 20. Which of the following needs a proof ?<\/strong><\/p>\n<p>(A) Theorem<\/p>\n<p>(B) Axiom<\/p>\n<p>(C) Definition<\/p>\n<p>(D) Postulate<\/p>\n<p><strong>Solution: <\/strong>(A)<\/p>\n<p>The statements that needs a proof are called propositions or theorems.<\/p>\n<p><strong>Question 21. Euclid stated that all right angles are equal to each other in the form of<\/strong><\/p>\n<p>(A) an axiom<\/p>\n<p>(B) a definition<\/p>\n<p>(C) a postulate<\/p>\n<p>(D) a proof<\/p>\n<p><strong>Solution: <\/strong>(C)<\/p>\n<p>Euclid stated that all right angles are equal to each other in the form of a postulate.<\/p>\n<p><strong>Question 22. \u2018Lines are parallel, if they do not intersect\u2019 is stated in the form of<\/strong><\/p>\n<p>(A) an axiom<\/p>\n<p>(B) a definition<\/p>\n<p>(C) a postulate<\/p>\n<p>(D) a proof<\/p>\n<p><strong>Solution: <\/strong>(B)<\/p>\n<p>\u2018Lines are parallel, if they do not intersect\u2019 is the definition of parallel lines.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"NCERT_Exemplar_Class_9_Maths_Chapter_5_Exercise_52\"><\/span>NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Question 1. <\/strong>Euclidean geometry is valid only for curved surfaces<\/p>\n<p><strong>Solution: <\/strong>False<\/p>\n<p>Because Euclidean geometry is valid only for the figures in the plane but on the curved surfaces, it fails.<\/p>\n<p><strong>Question 2. <\/strong>The boundaries of the solids are curves.<\/p>\n<p><strong>Solution: <\/strong>Because the boundaries of the solids are surfaces.<\/p>\n<p><strong>Question 3. <\/strong>The edges of a surface are curves.<\/p>\n<p><strong>Solution: <\/strong>False<\/p>\n<p>Because the edges of surfaces are lines.<\/p>\n<p><strong>Question 4. <\/strong>The things which are double of the same thing are equal to one another<\/p>\n<p><strong>Solution: <\/strong>True<\/p>\n<p>Since, it is one of the Euclid\u2019s axiom.<\/p>\n<p><strong>Question 5. <\/strong>If a quantity B is a part of another quantity A, then A can be written as the sum of B and some third quantity C.<\/p>\n<p><strong>Solution: <\/strong>True<\/p>\n<p>Since, it is one of the Euclid\u2019s axiom.<\/p>\n<p><strong>Question 6. <\/strong>The statements that are proved are called axioms.<\/p>\n<p><strong>Solution: <\/strong>False<\/p>\n<p>Because the statements that are proved are called theorems.<\/p>\n<p><strong>Question 7. <\/strong>\u201cFor every line l and for every point P not lying on a given line l, there exits a unique line m passing though P and parallel to l is known as Playfair\u2019s axiom.<\/p>\n<p><strong>Solution: <\/strong>True<\/p>\n<p>Since, it is an equivalent version of Euclid\u2019s fifth postulate and it is known as Playfair\u2019s axiom.<\/p>\n<p><strong>Question 8. <\/strong>Two distinct intersecting lines cannot be parallel to the same line.<\/p>\n<p><strong>Solution: <\/strong>True<\/p>\n<p>Since, it is an equivalent version of Euclid\u2019s fifth postulate.<\/p>\n<p><strong>Question 9. <\/strong>Attempt to prove Euclid\u2019s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.<\/p>\n<p><strong>Solution: <\/strong>True<\/p>\n<p>All attempts to prove the fifth postulate as a theorem led to a great achievement in the creation of several other geometries. These geometries are quite different from Euclidean geometry and are called non-Euclidean geometry.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"NCERT_Exemplar_Class_9_Maths_Chapter_5_Exercise_53\"><\/span>NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.3<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Question 1. <\/strong>Two salesmen make equal sales during the month of August. In September, each salesmen doubles his sale of the month of August. Compare their sales in September.<\/p>\n<p><strong>Solution: <\/strong>Let the equal sales of two salesmen in August be y. In September, each salesman doubles his sale of August.<\/p>\n<p>Thus, sale of first salesman is 2y and sale of second salesman is 2y.<\/p>\n<p>According to Euclid\u2019s axioms, things which are double of the same things are equal to one another.<\/p>\n<p>So, in September their sales are again equal.<\/p>\n<p><strong>Question 2.<\/strong><\/p>\n<p>It is known that x + y = 10 and that x = z. Show that z + y = 10.<\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>We have, x + y = 10 \u2026(i)<\/p>\n<p>and x = z \u2026(ii)<\/p>\n<p>On adding y to both sides, we have x + y = z + y \u2026. (iii)<\/p>\n[ \u2235 If equals are added to equals, the wholes are equal] From (i) and (iii), we get z + y = 10<\/p>\n<p><strong>Question 3. <\/strong>Look at the given figure. Show that length AH &gt; sum of lengths of AB + BC + CD.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-708284\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-1.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-1\" width=\"234\" height=\"37\" \/><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>From the given figure, we have<\/p>\n<p>AB + BC + CD = AD<\/p>\n[AB, BC and CD are the parts of AD]\n<p>Since, AD is also the part of AH.<\/p>\n<p>AH &gt; AD [ \u2235 The whole is greater than the part]\n<p>So, length AH &gt; sum of lengths of AB + BC + CD.<\/p>\n<p><strong>Question 4. <\/strong>In the given figure, we have AB = BC, BX = BY. Show that AX = CY.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-708285\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-2.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-2\" width=\"116\" height=\"111\" \/><\/p>\n<p><strong>Solution: <\/strong>Given, AB = BC \u2026(i)<\/p>\n<p>and BX = BY \u2026(ii)<\/p>\n<p>On subtracting (ii) from (i), we get AB \u2013 BX = BC \u2013 BY<\/p>\n[\u2235 If equals are subtracted from equals, the remainders are equal]\n<p>\u2234 AX = CY<\/p>\n<p><strong>Question 5. <\/strong>In the given figure, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708286\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-3.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-3\" width=\"108\" height=\"113\" \/><\/p>\n<p><strong>Solution: <\/strong>We have, X is the mid-point of AC.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708287\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-4.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-4\" width=\"337\" height=\"249\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-4.png 337w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-4-300x222.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><\/p>\n<p><strong>Question 6. <\/strong>In the given figure, we have<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-708288\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-5-300x152-1.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-5\" width=\"300\" height=\"152\" \/><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-708289\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-6.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-6\" width=\"336\" height=\"166\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-6.png 336w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-6-300x148.png 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><\/p>\n<p><strong>Question 7. <\/strong>In the given figure, we have \u22201 = \u22202 and \u22202 = \u22203. Show that \u22201 = \u22203.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708290\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-7.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-7\" width=\"184\" height=\"184\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-7.png 184w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-7-150x150.png 150w\" sizes=\"(max-width: 184px) 100vw, 184px\" \/><br \/>\n<strong>Solution: <\/strong>We have, \u22201 = \u22202 and \u22202 = \u22203 \u21d2 \u22201 = \u22203 [ \u2235 Things which are equal to the same thing are equal to one another]\n<p><strong>Question 8. <\/strong>In the given figure, we have \u22201 = \u22203 and \u22202 = \u22204. Show that \u2220A = \u2220C.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708291\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-8.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-8\" width=\"180\" height=\"179\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-8.png 180w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-8-150x150.png 150w\" sizes=\"(max-width: 180px) 100vw, 180px\" \/><br \/>\n<strong>Solution: <\/strong>Given \u22201 = \u22203 \u2026(i)<\/p>\n<p>\u22202 = \u22204 \u2026(ii)<\/p>\n<p>Adding (i) and (ii), we get \u22201 + \u22202 = \u22203 + \u22204<\/p>\n[\u2235 If equals are added to equals, then wholes are also equal]\n<p>\u21d2 \u2220A = \u2220C<\/p>\n<p><strong>Question 9. <\/strong>In the given figure, we have \u2220ABC = \u2220ACB, \u22203 = \u22204. Show that \u22201 = \u22202.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708292\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-9.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-9\" width=\"102\" height=\"110\" \/><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given \u2220ABC = \u2220ACB \u2026(i)<\/p>\n<p>and \u2220A = \u22203 \u2026(ii)<\/p>\n<p>Subtracting (ii) from (i), we get \u2220ABC \u2013 \u22204 = \u2220ACB \u2013 \u22203<\/p>\n[ \u2235 If equals are subtracted from equals, then remainders are also equal]\n<p>\u21d2 \u22201 = \u22202<\/p>\n<p><strong>Question 10. <\/strong>In the given figure, we have AC = DC, CB = CE. Show that AB = DE.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708293\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-10.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-10\" width=\"232\" height=\"163\" \/><br \/>\n<strong>Solution: <\/strong>We have, AC = DC \u2026(i)<\/p>\n<p>and CB = CE \u2026(ii)<\/p>\n<p>Adding (i) and (ii), we get<\/p>\n<p>AC + CB = DC + CE<\/p>\n[ \u2235 If equals are added to equals, then wholes are also equal]\n<p>\u21d2 AB = DE<\/p>\n<p><strong>Question 11. <\/strong>In the given figure, if OX = <span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\">1<span id=\"MathJax-Span-5\" class=\"mn\">2XY, PX = <span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\">1<span id=\"MathJax-Span-10\" class=\"mn\">2XZ and OX= PX, show that XY= XZ<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708294\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-11.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-11\" width=\"102\" height=\"116\" \/><br \/>\n<strong>Solution: <\/strong>Given OX = <span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\">1<span id=\"MathJax-Span-15\" class=\"mn\">2XY \u21d2 20X = XY \u2026(i)<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\">PX = <span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\">1<span id=\"MathJax-Span-20\" class=\"mn\">2XZ \u21d2 2PX = XZ \u2026(ii)<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\">and OX = PX \u2026(iii)<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\">multiplying (iii) by 2, we get<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\">2OX = 2PX<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\">[\u2235 Things which are double of the same things are equal to one another]\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\">\u21d2 XY = XZ [From (i) and (ii)]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\"><strong>Question 12. <\/strong>In the given figure<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708295\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-12.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-12\" width=\"172\" height=\"145\" \/><br \/>\n(i) AB = BC, M is the mid-point of AB and N is the mid-point of BC. Show that AM = NC.<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\">(ii) BM = BN, M is the mid-point of AB and N is the mid-point of BC. Show that AB = BC.<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\"><strong>Solution:<\/strong><br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\">(i): Given, AB = BC \u2026(1)<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\">M is the mid-point of AB.<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\"><img loading=\"lazy\" class=\"alignnone size-full wp-image-708296\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-13-300x41-1.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-13\" width=\"300\" height=\"41\" \/><br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\">and N is the mid-point of BC.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-708297\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-14-300x42-1.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-14\" width=\"300\" height=\"42\" \/><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\">Multiplying both sides of (1) by <span id=\"MathJax-Element-5-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-21\" class=\"math\"><span id=\"MathJax-Span-22\" class=\"mrow\"><span id=\"MathJax-Span-23\" class=\"mfrac\"><span id=\"MathJax-Span-24\" class=\"mn\">1<span id=\"MathJax-Span-25\" class=\"mn\">2, we get<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\"><span id=\"MathJax-Element-5-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-21\" class=\"math\"><span id=\"MathJax-Span-22\" class=\"mrow\"><span id=\"MathJax-Span-23\" class=\"mfrac\"><span id=\"MathJax-Span-24\" class=\"mn\"><span id=\"MathJax-Span-25\" class=\"mn\"><img loading=\"lazy\" class=\"alignnone size-full wp-image-708298\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclids-Geometry-15.png\" alt=\"NCERT-Exemplar-Class-9-Maths-Chapter-5-Introduction-to-Euclid\u2019s-Geometry-15\" width=\"90\" height=\"41\" \/><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\"><span id=\"MathJax-Element-5-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-21\" class=\"math\"><span id=\"MathJax-Span-22\" class=\"mrow\"><span id=\"MathJax-Span-23\" class=\"mfrac\"><span id=\"MathJax-Span-24\" class=\"mn\"><span id=\"MathJax-Span-25\" class=\"mn\">[ \u2235 Things which are halves of the same things are equal to one another]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mn\"><span id=\"MathJax-Span-5\" class=\"mn\"><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"mfrac\"><span id=\"MathJax-Span-9\" class=\"mn\"><span id=\"MathJax-Span-10\" class=\"mn\"><span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mfrac\"><span id=\"MathJax-Span-14\" class=\"mn\"><span id=\"MathJax-Span-15\" class=\"mn\"><span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-16\" class=\"math\"><span id=\"MathJax-Span-17\" class=\"mrow\"><span id=\"MathJax-Span-18\" class=\"mfrac\"><span id=\"MathJax-Span-19\" class=\"mn\"><span id=\"MathJax-Span-20\" class=\"mn\"><span id=\"MathJax-Element-5-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-21\" class=\"math\"><span id=\"MathJax-Span-22\" class=\"mrow\"><span id=\"MathJax-Span-23\" class=\"mfrac\"><span id=\"MathJax-Span-24\" class=\"mn\"><span id=\"MathJax-Span-25\" class=\"mn\">\u21d2 AM = NC [Using (2) and (3)]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>(ii) Given, BM = BN \u2026(1)<\/p>\n<p>M is the mid-point of AB.<\/p>\n<p>\u2234 AM = BM = <span id=\"MathJax-Element-6-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-26\" class=\"math\"><span id=\"MathJax-Span-27\" class=\"mrow\"><span id=\"MathJax-Span-28\" class=\"mfrac\"><span id=\"MathJax-Span-29\" class=\"mn\">1<span id=\"MathJax-Span-30\" class=\"mn\">2AB<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-6-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-26\" class=\"math\"><span id=\"MathJax-Span-27\" class=\"mrow\"><span id=\"MathJax-Span-28\" class=\"mfrac\"><span id=\"MathJax-Span-29\" class=\"mn\"><span id=\"MathJax-Span-30\" class=\"mn\">\u21d2 2AM = 2BM = AB \u2026(2)<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-6-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-26\" class=\"math\"><span id=\"MathJax-Span-27\" class=\"mrow\"><span id=\"MathJax-Span-28\" class=\"mfrac\"><span id=\"MathJax-Span-29\" class=\"mn\"><span id=\"MathJax-Span-30\" class=\"mn\">and N is the mid-point of BC.<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-6-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-26\" class=\"math\"><span id=\"MathJax-Span-27\" class=\"mrow\"><span id=\"MathJax-Span-28\" class=\"mfrac\"><span id=\"MathJax-Span-29\" class=\"mn\"><span id=\"MathJax-Span-30\" class=\"mn\">\u2234 BN = NC = <span id=\"MathJax-Element-7-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-31\" class=\"math\"><span id=\"MathJax-Span-32\" class=\"mrow\"><span id=\"MathJax-Span-33\" class=\"mfrac\"><span id=\"MathJax-Span-34\" class=\"mn\">1<span id=\"MathJax-Span-35\" class=\"mn\">2BC<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-6-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-26\" class=\"math\"><span id=\"MathJax-Span-27\" class=\"mrow\"><span id=\"MathJax-Span-28\" class=\"mfrac\"><span id=\"MathJax-Span-29\" class=\"mn\"><span id=\"MathJax-Span-30\" class=\"mn\"><span id=\"MathJax-Element-7-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-31\" class=\"math\"><span id=\"MathJax-Span-32\" class=\"mrow\"><span id=\"MathJax-Span-33\" class=\"mfrac\"><span id=\"MathJax-Span-34\" class=\"mn\"><span id=\"MathJax-Span-35\" class=\"mn\">\u21d2 2BN = 2NC = BC \u2026(3)<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-6-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-26\" class=\"math\"><span id=\"MathJax-Span-27\" class=\"mrow\"><span id=\"MathJax-Span-28\" class=\"mfrac\"><span id=\"MathJax-Span-29\" class=\"mn\"><span id=\"MathJax-Span-30\" class=\"mn\"><span id=\"MathJax-Element-7-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-31\" class=\"math\"><span id=\"MathJax-Span-32\" class=\"mrow\"><span id=\"MathJax-Span-33\" class=\"mfrac\"><span id=\"MathJax-Span-34\" class=\"mn\"><span id=\"MathJax-Span-35\" class=\"mn\">multiplying both sides of (1) by 2, we get<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-6-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-26\" class=\"math\"><span id=\"MathJax-Span-27\" class=\"mrow\"><span id=\"MathJax-Span-28\" class=\"mfrac\"><span id=\"MathJax-Span-29\" class=\"mn\"><span id=\"MathJax-Span-30\" class=\"mn\"><span id=\"MathJax-Element-7-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-31\" class=\"math\"><span id=\"MathJax-Span-32\" class=\"mrow\"><span id=\"MathJax-Span-33\" class=\"mfrac\"><span id=\"MathJax-Span-34\" class=\"mn\"><span id=\"MathJax-Span-35\" class=\"mn\">2 BM = 2 BN<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-6-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-26\" class=\"math\"><span id=\"MathJax-Span-27\" class=\"mrow\"><span id=\"MathJax-Span-28\" class=\"mfrac\"><span id=\"MathJax-Span-29\" class=\"mn\"><span id=\"MathJax-Span-30\" class=\"mn\"><span id=\"MathJax-Element-7-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-31\" class=\"math\"><span id=\"MathJax-Span-32\" class=\"mrow\"><span id=\"MathJax-Span-33\" class=\"mfrac\"><span id=\"MathJax-Span-34\" class=\"mn\"><span id=\"MathJax-Span-35\" class=\"mn\">[ \u2235 Things which are double of the same thing are equal to one another]\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span id=\"MathJax-Element-6-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-26\" class=\"math\"><span id=\"MathJax-Span-27\" class=\"mrow\"><span id=\"MathJax-Span-28\" class=\"mfrac\"><span id=\"MathJax-Span-29\" class=\"mn\"><span id=\"MathJax-Span-30\" class=\"mn\"><span id=\"MathJax-Element-7-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-31\" class=\"math\"><span id=\"MathJax-Span-32\" class=\"mrow\"><span id=\"MathJax-Span-33\" class=\"mfrac\"><span id=\"MathJax-Span-34\" class=\"mn\"><span id=\"MathJax-Span-35\" class=\"mn\">\u21d2 AB = BC [Using (2) and (3)]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"NCERT_Exemplar_Class_9_Maths_Chapter_5_Exercise_54\"><\/span>NCERT Exemplar Class 9 Maths Chapter 5 Exercise 5.4<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Question 1. <\/strong>Read the following statement:<\/p>\n<p>An equilateral triangle is a polygon made up of three line segments out of which two line segments are equal to the third one and all its angles are 60\u00b0 each. Define the terms used in this definition which you feel necessary. Are there any undefined terms in this? Can you justify that all sides and all angles are equal in a equilateral triangle.<\/p>\n<p><strong>Solution: <\/strong>The terms need to be defined are<\/p>\n<ol>\n<li><strong>Polygon :<\/strong> A closed figure bounded by three or more line Segments.<\/li>\n<li><strong>Line segment :<\/strong> Part of a line with two end points.<\/li>\n<li><strong>Line:<\/strong> Undefined term.<\/li>\n<li><strong>Point:<\/strong> Undefined term.<\/li>\n<li><strong>Angle:<\/strong> A figure formed by two rays with one common initial point.<\/li>\n<li><strong>Acute angle :<\/strong> Angle whose measure is between 0\u00b0 to 90\u00b0.<\/li>\n<\/ol>\n<p>Here undefined terms are line and point. All the angles of equilateral triangle are 60\u00b0 each (given). Two line segments are equal to the third one (given).<\/p>\n<p>\u201cAccording to Euclid\u2019s axiom, \u201cthings which are equal to the same things are equal to one another\u201d, we conclude that all three sides of an equilateral triangle are equal.<\/p>\n<p><strong>Question 2. <\/strong>Study the following statements:<\/p>\n<p>\u201cTwo intersecting lines cannot be perpendicular to the same line.\u201d Check whether it is an equivalent version to the Euclid\u2019s fifth postulate. [Hint: Identify the two intersecting lines \/ and m and the line n in the above statement.]\n<p><strong>Solution: <\/strong>Two equivalent versions of Euclid\u2019s fifth postulate are as follows:<\/p>\n<ol>\n<li>For every line l and for every point P not lying on l, there exists a unique line m passing through P and parallel to l.<\/li>\n<li>Two distinct intersecting lines cannot be parallel to the same line.<\/li>\n<\/ol>\n<p>From above two statements it is clear that given statement is not an equivalent version to the Euclid\u2019s fifth postulate.<\/p>\n<p><strong>Question 3. <\/strong>Read the following statements which are taken as axioms:<\/p>\n<p>(i) If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.<\/p>\n<p>(ii) If a transversal intersect two parallel lines, then alternate interior angles are equal.<\/p>\n<p>Is this system of axioms consistent ? Justify your answer.<\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>As we know that, if a transversal intersects two parallel lines, then each pair of corresponding angles are equal, then first is false, so, not an axiom. Also, if a transversal intersects two parallel lines, then each pair of alternate interior angles are equal, then second is true so, it is an axiom.<\/p>\n<p>So, in given statements, first is false and second is an axiom. Thus, given system of axioms is not consistent.<\/p>\n<p><strong>Question 4. <\/strong>Read the following two statements which are taken as axioms:<\/p>\n<ol>\n<li> If two lines intersect each other, then the vertically opposite angles are not equal.<\/li>\n<li>If a ray stands on a line, then the sum of two adjacent angles, so formed is equal to 180\u00b0. Is this system of axioms consistent ? Justify your answer.<\/li>\n<\/ol>\n<p><strong>Solution: <\/strong>As we know that, if two lines intersect each other, then the vertically opposite angles are equal, then first is false, so, not an axiom. Also, if a ray stands on a line, then the sum of two adjacent angles so formed is equal to 180\u00b0, then second is true so, it is an axiom.<\/p>\n<p>So, in given statements, first is false and second is an axiom. Thus, given system of axioms is not consistent.<\/p>\n<p><strong>Question 5. <\/strong>Read the following axioms:<\/p>\n<p>(i) Things which are equal to the same thing are equal to one another.<\/p>\n<p>(ii) If equals are added to equals, the wholes are equal.<\/p>\n<p>(iii) Things which are double of the same thing are equal to one another.<\/p>\n<p>Check whether the given system of axioms is consistent or inconsistent.<\/p>\n<p><strong>Solution: <\/strong>Since, the given three axioms are Euclid\u2019s axioms.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Real-World_Applications_of_Euclids_Geometry\"><\/span>Real-World Applications of Euclid\u2019s Geometry<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Euclid\u2019s Geometry is not only theoretical but also finds its applications in the real world:<\/p>\n<ol>\n<li><strong>Architecture and Design<\/strong>: Understanding the basic principles of Euclidean geometry is essential in fields like architecture, where shapes and spaces need to be constructed based on geometric principles.<\/li>\n<li><strong>Navigation and Mapping<\/strong>: Concepts from Euclidean geometry are still used today in cartography and navigation systems to map out the Earth\u2019s surface.<\/li>\n<\/ol>\n<p>Including such real-world applications in your study can help you grasp the importance and utility of what you&#8217;re learning.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Why_Study_Euclids_Geometry_with_NCERT_Exemplar_Solutions\"><\/span>Why Study Euclid\u2019s Geometry with NCERT Exemplar Solutions?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The <strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-9\/maths\/\">NCERT Exemplar Solutions for Class 9 Maths<\/a> Chapter 5<\/strong> help students:<\/p>\n<ol>\n<li><strong>Master Complex Concepts<\/strong>: Euclidean geometry might seem abstract, but our solutions break down the concepts into easy-to-understand steps.<\/li>\n<li><strong>Prepare for Competitive Exams<\/strong>: Concepts from Euclid\u2019s Geometry are important not just for school exams but also for competitive exams like <strong>JEE<\/strong>.<\/li>\n<li><strong>Develop Critical Thinking<\/strong>: Euclid\u2019s approach helps students develop logical reasoning skills which are critical for mathematics as a subject.<\/li>\n<\/ol>\n<h2><span class=\"ez-toc-section\" id=\"Introduction_to_Euclids_Geometry_FAQs\"><\/span>Introduction to Euclids Geometry FAQ&#8217;s<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Is_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_5_suitable_for_CBSE_students\"><\/span>Is NCERT Exemplar Solutions for Class 9 Maths Chapter 5 suitable for CBSE students?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tNCERT Exemplar Solutions have been prescribed for years as a complete source of information to CBSE students, to develop their analytical skills. They have proven to be essential for learning the syllabus and developing the confidence that is required to face their exams. The NCERT Exemplar Solutions for Class 9 Maths Chapter 5 explains the steps with precision, without missing out on essential aspects of solving a question. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Where_can_I_download_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_5\"><\/span>Where can I download NCERT Exemplar Solutions for Class 9 Maths Chapter 5?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tNCERT Exemplar Solutions for Class 9 Maths Chapter 5 Statistics are provided on the Infinity Learn website, which is considered to be one of the most important study materials for students studying in Class 9. The solutions provided at Infinity Learn are formulated in such a way that every step is explained clearly and in detail. The Solutions for Class 9 Maths NCERT are prepared by the subject experts to help students in their board exam preparation. It is very important for the students to get well versed with these solutions to get a good score in the Class 9 examination. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_meaning_of_Euclidean_geometry_according_to_NCERT_Exemplar_Solutions_for_Class_9_Maths_Chapter_5\"><\/span>What is the meaning of Euclidean geometry according to NCERT Exemplar Solutions for Class 9 Maths Chapter 5?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tEuclidean geometry is the study of geometrical shapes and figures based on different axioms and theorems. It is basically introduced for flat surfaces. It is better explained especially for the shapes of geometrical figures and planes. By referring to NCERT Exemplar Solutions for Class 9 Maths Chapter 5 students can score well in exams.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Is NCERT Exemplar Solutions for Class 9 Maths Chapter 5 suitable for CBSE students?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"NCERT Exemplar Solutions have been prescribed for years as a complete source of information to CBSE students, to develop their analytical skills. They have proven to be essential for learning the syllabus and developing the confidence that is required to face their exams. The NCERT Exemplar Solutions for Class 9 Maths Chapter 5 explains the steps with precision, without missing out on essential aspects of solving a question.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Where can I download NCERT Exemplar Solutions for Class 9 Maths Chapter 5?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"NCERT Exemplar Solutions for Class 9 Maths Chapter 5 Statistics are provided on the Infinity Learn website, which is considered to be one of the most important study materials for students studying in Class 9. The solutions provided at Infinity Learn are formulated in such a way that every step is explained clearly and in detail. The Solutions for Class 9 Maths NCERT are prepared by the subject experts to help students in their board exam preparation. It is very important for the students to get well versed with these solutions to get a good score in the Class 9 examination.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the meaning of Euclidean geometry according to NCERT Exemplar Solutions for Class 9 Maths Chapter 5?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Euclidean geometry is the study of geometrical shapes and figures based on different axioms and theorems. It is basically introduced for flat surfaces. It is better explained especially for the shapes of geometrical figures and planes. By referring to NCERT Exemplar Solutions for Class 9 Maths Chapter 5 students can score well in exams.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Introduction to Euclid\u2019s Geometry is a crucial chapter for students preparing for Class 9 Maths. It introduces the foundational concepts [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"NCERT Exemplar Solutions","_yoast_wpseo_title":"NCERT Exemplar Solutions for Class 9 Maths Chapter 5 | Euclid\u2019s Geometry","_yoast_wpseo_metadesc":"Get step-by-step NCERT Exemplar Solutions for Class 9 Maths Chapter 5: Introduction to Euclid\u2019s Geometry. Download free PDFs and explore detailed solutions with real-world applications and YouTube videos for better understanding.","custom_permalink":"study-materials\/ncert-exemplar-solutions\/class-9\/maths\/chapter-5-introduction-to-euclids-geometry\/"},"categories":[152,159,105,21],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Exemplar Solutions for Class 9 Maths Chapter 5 | Euclid\u2019s Geometry<\/title>\n<meta name=\"description\" content=\"Get step-by-step NCERT Exemplar Solutions for Class 9 Maths Chapter 5: Introduction to Euclid\u2019s Geometry. 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