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

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

    Points on a plane

  2. 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

    A line AB on a plane

  3. 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

    Planes illustrated with imagination

  4. 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

    A ray of line

  5. 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

    Figure showing angles and way of naming them

  6. 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 remains constant. OA=OB=OC

    Circle in a Plane

    Point A,O,C,B on the plane whose distance from a fix point remains constant. OA=OB=OC

  7. 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 quadileteral

    Point a,B,C,D Form a Quadileteral

    Point A,B,C,D in a plane with four line segments 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 they are extended to the infinity.

    Two Parallel Line M,N

    Two parallel line m,n. The parallel lines never meet even if they are extended to the infinity.

    In fig m and n parallel.

  2. 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,if they from a right angle.

    Perpendicular Lines Forming Right Angle

    AB and CD lying the same plane are said to be perpendiculer,if they from a right angle.

  3. 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 distance point,say A and B on line are given end point of A and B is line segment

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

    Give point A and B a line-segment is part of line.when two distance point,say A and B on line are given end point of A and B is line segment

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

  4. 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

    Circle with center O and radius OP

  5. 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

    Square is a quadiland with four equal sides.

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