Page 216 - ICSE Math 6

Example 5: Write the number of lines of symmetry (wherever possible) for the following.
(a) A line segment of length 10 cm.
(b) A rectangle of length 6 cm and breadth 3 cm.
(c) A circle of radius 6.6 cm.
(d) A triangle with sides 3 cm, 4.5 cm and 7 cm.
Solution: (a) A line segment of any length has 2 lines of symmetry.
(b) A rectangle has only 2 lines of symmetry.
(c) A circle has infinite lines of symmetry.
(d) A scalene triangle is nonsymmetric and hence it has 0 line of symmetry.

To Construct a Point Symmetric to a Given Point with Respect to a Line

Given a point A and a line PQ, we will construct a point symmetric A
to the point A with respect to the line PQ. To do so, follow the steps
given below.
P Q

A

Step 1: From point A, draw AB perpendicular to PQ.
P B Q

A
Step 2: Extend AB and draw an arc with centre at B and radius
AB such that AB = BC. Thus, point C is symmetric to P B Q
point A.
C
To Construct a Line with Respect to Which Two Given Points are Symmetric

Given two points A and B, we will construct a line so that the given
two points are symmetric. To do so, follow the steps given below. A B
Step 1: Join the points A and B.
A B

P
Step 2: Draw the perpendicular bisector PQ of line segment
AB. This perpendicular bisector PQ is the required line A B
of symmetry with respect to which points A and B are
symmetric. Q

EXERCISE

1. Write True or False.
(a) The letter V has 2 lines of symmetry. (b) The letter M has 1 line of symmetry.
(c) An arrowhead has 1 line of symmetry. (d) An isosceles triangle has 2 lines of symmetry.
(e) A line segment has infinite lines of symmetry.

200