Give a definition for each of the following terms. Are there other terms that need to be defined first¿? What are they and how might you define them?
(i) Parallel lines
(ii) Perpendicular lines
(iii) Line segment
(iv) Radius of a circle
(v) Square
Answers
Yes, we need to have an idea about the terms like point, line, ray, angle, plane, circle and quadrilateral, etc. before defining the required terms.
Definitions of the required terms are given below:
- (i) Parallel Lines:
Two lines l and m in a plane are said to be parallel, if they have no common point and we write them as l ॥ m.
- (ii) Perpendicular Lines:
Two lines p and q lying in the same plane are said to be perpendicular if they form a right angle and we write them as p ⊥ q.
- (iii) Line Segment:
A line segment is a part of line and having a definite length. It has two end-points.
- (iv) Radius of a circle :
The distance from the centre to a point on the circle is called the radius of the circle.
- (v) Square :
A quadrilateral in which all the four angles are right angles and all the four sides are equal is called a square.
(i) Parallel line - Two lines are said to be parallel when (a) They never meet or never intersect each other even if they are extended to the infinity. (b) they coplanar.
(ii) 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
(iii) 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.
(iv) Radius of a circle - 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.
(v) 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.