Question

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

Answer 1

(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 $AB\perp CD$

(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.