{"id":26533,"date":"2022-01-31T11:44:49","date_gmt":"2022-01-31T06:14:49","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=26533"},"modified":"2024-02-21T12:38:18","modified_gmt":"2024-02-21T07:08:18","slug":"introduction-to-euclids-geometry-class-9-notes-maths-chapter-3","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-material\/cbse-notes\/class-9\/maths\/introduction-to-euclids-geometry-class-9-notes-maths-chapter-3\/","title":{"rendered":"Introduction to Euclid\u2019s Geometry Class 9 Notes Maths Chapter 3"},"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-material\/cbse-notes\/class-9\/maths\/introduction-to-euclids-geometry-class-9-notes-maths-chapter-3\/#CBSE_Class_9_Maths_Notes_Chapter_3_Introduction_to_Euclids_Geometry\" title=\"CBSE Class 9 Maths Notes Chapter 3 Introduction to Euclid\u2019s Geometry\">CBSE Class 9 Maths Notes Chapter 3 Introduction to Euclid\u2019s Geometry<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-material\/cbse-notes\/class-9\/maths\/introduction-to-euclids-geometry-class-9-notes-maths-chapter-3\/#NCERT_Notes_for_Class_9_Maths\" title=\"NCERT Notes for Class 9 Maths\">NCERT Notes for Class 9 Maths<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Class_9_Maths_Notes_Chapter_3_Introduction_to_Euclids_Geometry\"><\/span>CBSE Class 9 Maths Notes Chapter 3 Introduction to Euclid\u2019s Geometry<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1.<strong> Axioms or Postulates:<\/strong> Axioms or postulates are the assumptions which are obvious universal truths. They are not proved.<br \/>\nMainly postulates are used for especially geometry and axioms are used for especially algebra.<\/p>\n<p>2. <strong>Theorems:<\/strong> Theorems are statements which are proved using \u2018 definitions, axioms, previously proved statements and deductive reasoning.<\/p>\n<p>3. <strong>Euclid\u2019s Definitions, Axioms or Postulates<\/strong><\/p>\n<ul>\n<li>A point is that which has no part.<\/li>\n<li>A line is a breadthless length.<\/li>\n<li>The ends of a line are points.<\/li>\n<li>A straight line is a line which lies evenly with the points on itself.<\/li>\n<li>A surface is that which has length and breadth only.<\/li>\n<li>The edges of a surface are lines.<\/li>\n<li>A plane surface is a surface which lies evenly with the straight lines on itself.<\/li>\n<\/ul>\n<p>4. <strong>Undefined Terms:<\/strong> There are some terms like point etc which have no definitions, these terms are called undefined terms.<br \/>\nIn geometry, a point, a line and a plane (in Euclid\u2019s words, a plane surface) are undefined terms.<\/p>\n<p>5. <strong>Euclid\u2019s Axioms<\/strong><\/p>\n<ul>\n<li>Things which are equal to the same thing are equal to one another.<\/li>\n<li>If equals are added to equals, the wholes are equal.<\/li>\n<li>If equals are subtracted from equals, the remainders are equal.<\/li>\n<li>Things which coincide with one another are equal to one another.<\/li>\n<li>The whole is greater than the part.<\/li>\n<li>Things which are double of the same things are equal to one another.<\/li>\n<li>Things which are halves of the same things are equal to one another.<\/li>\n<\/ul>\n<p>6. <strong>Euclid\u2019s Five Postulates:<\/strong> Euclid\u2019s five postulates are given below<br \/>\n<strong>Postulate 1:<\/strong> A straight line may be drawn from any one point to any other point.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32649381317_c034b86645_o.png\" alt=\"Introduction to Euclids Geometry Class 9 Notes Maths Chapter 3 1\" width=\"224\" height=\"50\" \/><br \/>\nAxiom Given two distinct points, there is a unique line that passes through them.<\/p>\n<p><strong>Postulate 2:<\/strong> A terminated line can be produced indefinitely. Euclid\u2019s terminated line is called a line segment. So, according to the present day terms, \u2018A line segment can be extended on either side to form a line\u2019.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32649381287_2a7668f13d_o.png\" alt=\"Introduction to Euclids Geometry Class 9 Notes Maths Chapter 3 2\" width=\"246\" height=\"87\" \/><\/p>\n<p><strong>Postulate 3:<\/strong> A circle can be drawn with any centre and any radius.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32649381267_1a88ee5645_o.png\" alt=\"Introduction to Euclids Geometry Class 9 Notes Maths Chapter 3 3\" width=\"163\" height=\"153\" \/><\/p>\n<p><strong>Postulate 4:<\/strong> All right angles are equal to one another.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47538874732_94c74c5e58_o.png\" alt=\"Introduction to Euclids Geometry Class 9 Notes Maths Chapter 3 4\" width=\"314\" height=\"173\" \/><br \/>\nIf \u22201 = 90\u00b0<br \/>\nand \u22202 = 90\u00b0<br \/>\n\u22201 = \u22202<\/p>\n<p><strong>Postulate 5:<\/strong> If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.<\/p>\n<p>e.g., The line PQ falls on lines AB and CD such that the sum of the interior angles 1 and 2 is less than 180\u00b0 on the left side of PQ. Therefore, the lines AB and CD will eventually intersect on the left side of PQ.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32649381247_4c0c685158_o.png\" alt=\"Introduction to Euclids Geometry Class 9 Notes Maths Chapter 3 5\" width=\"297\" height=\"202\" \/><br \/>\nNote: Two distinct lines cannot have more than one point in common.<\/p>\n<p>7. <strong>Equivalent Versions of Euclid\u2019s Fifth Postulate:<\/strong> \u2018For every line l and for every point P not lying on l, there exists a unique line m passing through P and parallel to \u2018l\u2019.<br \/>\nThis result can also be stated in the following form.<br \/>\nTwo distinct intersecting lines cannot be parallel to the same line.<\/p>\n<div class=\"featured-snippet\">\n<h3><span class=\"ez-toc-section\" id=\"NCERT_Notes_for_Class_9_Maths\"><\/span>NCERT Notes for Class 9 Maths<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>Chapter 1 Number Systems Class 9 Notes<\/li>\n<li>Chapter 2 Polynomials Class 9 Notes<\/li>\n<li>Chapter 3 Introduction to Euclid\u2019s Geometry Class 9 Notes<\/li>\n<li>Chapter 4 Lines and Angles Class 9 Notes<\/li>\n<li>Chapter 5 Triangles Class 9 Notes<\/li>\n<li>Chapter 6 Coordinate Geometry Class 9 Notes<\/li>\n<li>Chapter 7 Heron\u2019s Formula Class 9 Notes<\/li>\n<li>Chapter 8 Linear Equations in Two Variables Class 9 Notes<\/li>\n<li>Chapter 9 Quadrilaterals Class 9 Notes<\/li>\n<li>Chapter 10 Areas of Parallelograms and Triangles Class 9 Notes<\/li>\n<li>Chapter 11 Circles Class 9 Notes<\/li>\n<li>Chapter 12 Constructions Class 9 Notes<\/li>\n<li>Chapter 13 Surface Areas and Volumes Class 9 Notes<\/li>\n<li>Chapter 14 Statistics Class 9 Notes<\/li>\n<li>Chapter 15 Probability Class 9 Notes<\/li>\n<\/ul>\n<\/div>\n<p>We hope the given <a href=\"https:\/\/infinitylearn.com\/surge\/cbse-notes-class-9-maths\/\">CBSE Class 9 Maths Notes<\/a> Chapter 3 Introduction to Euclid\u2019s Geometry Pdf free download will help you. If you have any query regarding NCERT Class 9 Maths Notes Chapter 3 Introduction to Euclid\u2019s Geometry, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>CBSE Class 9 Maths Notes Chapter 3 Introduction to Euclid\u2019s Geometry 1. Axioms or Postulates: Axioms or postulates are the [&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":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Get Introduction to Euclid\u2019s Geometry Class 9 Notes Maths Chapter 3 on Infinity Learn.","custom_permalink":"study-material\/cbse-notes\/class-9\/maths\/introduction-to-euclids-geometry-class-9-notes-maths-chapter-3\/"},"categories":[92,13,21],"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>Introduction to Euclid\u2019s Geometry Class 9 Notes Maths Chapter 3 - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Get Introduction to Euclid\u2019s Geometry Class 9 Notes Maths Chapter 3 on Infinity Learn.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/study-material\/cbse-notes\/class-9\/maths\/introduction-to-euclids-geometry-class-9-notes-maths-chapter-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Introduction to Euclid\u2019s Geometry Class 9 Notes Maths Chapter 3 - 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