NCERT Class 9 Solutions: Introduction To Euclid's Geometry (Chapter 5) Exercise 5.1 – Part 2

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Q-2 Give a definition for each of the following terms. Are there other terms that need to be defined first? What are they how might you define them?

  1. parallel lines

  2. perpendicular lines

  3. line segment

  4. radius of a circle

  5. square

Solution:

To define the terms given in the question we need to define the following terms first

  1. Point: - A small dot made by sharp pencil on a sheet paper gives an idea about a point. A point has no dimension, it has only position. Ideal point is not possible.

Points on a plane

Points

  1. Line: - A line is the set of points which has length only and no breadth. The basic concept about a line is that it should be straight and that it should extend in definitely in both the directions.

A line AB on a plane

A Line on a Plane

  1. Plane: - The surface of a smooth wall or the surfaces of a sheet of paper are close examples of a plane.

Planes illustrated with imagination

Illustration of Geometrical Planes

  1. Ray: - A part of line l which has only one end-point A and contains the point B is called a ray AB.

A ray of line

Ray AB

  1. Angle: - An angle is the union o two non-collinear rays with a common initial point.

Figure showing angles and way of naming them

Angles and Naming Angles

  1. Circle: - A circle is the set of all those points in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle.

OA = OB = OC = radius

Point A,O,C,B on the plane whose distance from a fix point r …

Circle in a Plane

  1. Quadrilateral: - A closed figure made of four line segment is called a quadrilateral

Point A,B,C,D in a plane with four line segments form a quad …

Point a,B,C,D Form a Quadileteral

  1. Parallel Lines: - Line which do not intersect each other anywhere are called parallel lines.

Two parallel line m,n. The parallel lines never meet even if …

Two Parallel Line M,N

In fig m and n parallel.

  1. Perpendicular lines: - Two lines AB and CD lying the same plane are said to be perpendicular, if they form a right angle. We write AB ┴ CD.

AB and CD lying the same plane are said to be perpendiculer, …

Perpendicular Lines Forming Right Angle

  1. Line-segment: - A line-segment is a part of line. When two distinct points, say A and B on a line are given, then the part of this line with end-points A and B is called the line-segment.

Give point A and B a line-segment is part of line.when two d …

Give Point a and B a Line-Segment is Part of Line

It is named as AB, AB and BA denote the same line-segment.

  1. Radius: - The distance from the centre to a point on the circle is called the radius of the circle. In the following figure OP is the radius.

Circle with center O and radius OP

Circle with Center 0

  1. Square: - A quadrilateral in which all the four angles are right angles and four sides are equal is called a square. ABCD is a square.

Square is a quadiland with four equal sides.

A Square ABCD