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Chapter 3 Coordinate Geometry RS Aggarwal Solution for Class 9th Maths

Introduction toEuclid’s Geometry

Question 1:

Exercise 3A

A theorem is a statement that requires a proof. Whereas, a basic fact which is taken for granted, without proof, is called an axiom.

Example of Theorem: Pythagoras Theorem

Example of axiom: A unique line can be drawn through any two points.

Question 2:

  1. Line segment: The straight path between two points is called a line segment.
  2. Ray: A line segment when extended indefinitely in one direction is called a ray.
  3. Intersecting Lines: Two lines meeting at a common point are called intersecting lines, i.e., they have a common point.
  4. Parallel Lines: Two lines in a plane are said to be parallel, if they have no common point, i.e., they do not meet at all.
  5. Half-line: A ray without its initial point is called a half-line.
  6. Concurrent lines: Three or more lines are said to be concurrent, if they intersect at the same point.
  7. Collinear points: Three or more than three points are said to be collinear, if they lie on the same line.
  8. Plane: A plane is a surface such that every point of the line joining any two points on it, lies on it.

Question 3:

  1. Six points: A,B,C,D,E,F
  2. Five line segments: , , , ,

  1. Four rays: , , ,

  1. Four lines: , , ,
  2. Four collinear points: M,E,G,B

Question 4:

    1. and their corresponding point of intersection is R. and their corresponding point of intersection is P.
    2. , , and their point of intersection is R.
    3. Three rays are: , ,
    4. Two line segments are: ,

Question 5:

  1. An infinite number of lines can be drawn to pass through a given point.
  2. One and only one line can pass through two given points.
  3. Two given lines can at the most intersect at one and only one point.
  4. , ,

Question 6:

  1. False
  2. False
  3. False
  4. True
  5. False
  6. True
  7. True
  8. True
  9. True
  10. False
  11. False
  12. True

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