Mathematics Class 9 English

  CBSE Class 09 Mathematics Revision Notes CHAPTER – 5 INTRODUCTION TO EUCLID’S GEOMETRY 1 Euclid’s Definitions, Axioms and Postulates 2 Equivalent Versions of Euclid’s Fifth Postulate The Greeks developed geometry is a systematic manner which Euclid (300 B.C.) a Greek mathematician, father of geometry introduced the method of proving mathematical results by using deductive logical reasoning and the previously proved result. The Geometry of plane figure is know as "Euclidean Geometry". Axioms : The basic facts which are taken for granted without proof are called axioms. Some Euclid's axioms are (i) Things which are equal to the same thing are equal to one another. i.e. a = b , b = c ⇒ a = c a = b , b = c ⇒ a = c (ii) If equals are added to equals, the wholes are equal i.e. a = b ⇒ a + c = b + c a = b ⇒ a + c = b + c (iii) If equals are subtracted from equals, the remainders are equal i.e. a = b ⇒ a − c = b − c a = b ⇒ a − c = b − c (iv) Things which coincide with one anot...

  CBSE Class 9 Mathematics NCERT Solutions CHAPTER 5 Introduction to Euclids Geometry(Ex. 5.1) 1. Which of the following statements are true and which are false ? Give reasons for your answers. (i) Only one line can pass through a single point. (ii) There are infinite number of lines which pass through two distinct points. (iii) A terminated line can be produced indefinitely on both the sides. (iv) If two circles are equal, then their radii are equal. (v) In Fig. 5.9, if AB = PQ and PQ = XY, then AB = XY Ans.(i) False Correct statement: Infinite many lines can pass through a single point. This is self-evident and can be seen visually by the student given below: (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. Through two points P and Q a unique line can be drawn. (iii) True Reason:  We need to consider Euclid’s Postulate 2: “A terminated line can be produced ...

  CBSE Class 09 Mathematics Revision Notes CHAPTER – 6 LINES AND ANGLES Basic Terms and Definitions Intersecting Lines and Non-intersecting Lines Pairs of Angles Parallel Lines and a Transversal  Lines Parallel to the same Line Angle Sum Property of a Triangle (1)  Point  - We often represent a point by a fine dot made with a fine sharpened pencil on a piece of paper. (2)  Line  - A line is completely known if we are given any two distinct points. Line AB is represented by as    AB ← →   AB ↔  . A line or a straight line extends indefinitely in both the directions. (3)  Line segment  - A part (or portion) of a line with two end points is called a line segment. (4)  Ray  - A part of line with one end point is called a ray.It usually denotes the direction of line (5)  Collinear points  - If three or more points lie on the same line, they are called collinear points, otherwise they are called non-collinear poin...