Page 261 - Ganit Kaushal

Ex 8. Below is a picture of the new Indian Parliament Building and its boundary.

(a) Does the outer boundary of the picture have reflection symmetry? If so, draw the lines of symmetry.
How many are there?
(b) Does it have rotational symmetry around its
centre? If so, find the angles of rotational
symmetry. What is the least angle of symmetry?
(NCERT)
Sol. (a) Yes, the outer boundary of the parliament building has reflection symmetry since
one half covers the other half when folded about the dotted line.
It has 3 lines of symmetry. They are drawn and shown by black dotted lines in
the adjacent figure.
(b) Yes, the given figure has rotational symmetry around its centre.
When we rotate it about 120°, 240°, and 360°, we get the original shape.
\ Angles of rotational symmetry = 120°, 240°, and 360°; least angle of symmetry = 120°.
Ex 9. How many lines of symmetry do the first five shapes of the Koch Snowflake sequence have? (see Ch-1)
How many angles of symmetry do they have? What is the least angle of symmetry? (NCERT)
Sol. Shape 1: The initial shape is an equilateral triangle, which has lines of symmetry = 3, number of angles
of symmetry = 3 (120°, 240°, 360°) and the least angle of symmetry = 120°.
Shape 2 to 5: After the first iteration, the triangle becomes a hexagonal star-like shape. It maintains
the symmetry of a hexagonal-like structure at each stage, which has lines of symmetry = 6, number of
angles of symmetry = 6 (60°, 120°, 180°, 240°, 300°, 360°), least angle of symmetry = 60°.
Ex 10. Find the lines of symmetry, angles of symmetry, least angle of symmetry for the following shapes:

(a) (b) (c) (NCERT)

Sol. (a) Lines of symmetry = 1, Only 1 angle of symmetry = 360° = least angle of symmetry (No rotational
symmetry)

(b) Lines of symmetry = 0, least angle of symmetry = 90°, angles of symmetry = 90°, 180°, 270°, 360°.
(c) Lines of symmetry = 6, angles of symmetry = 60°, 120°,180°, 240°, 300°, 360°, least angle of
symmetry = 60°.

Ex 11. Can we have a figure with rotational symmetry whose least angle of symmetry is 19°?
Sol. We know that the least angle of symmetry of a figure having rotational symmetry must be a divisor
of 360°. Since 19° is not a divisor of 360°, we cannot have a figure with rotational symmetry whose
least angle of symmetry is 19°.

Exercise 9.2

1. Find the order and angles of symmetry for the given figures about the point marked •. Also find the
least angle of symmetry and the number of lines of symmetry, and draw them if any.

(a) (b)

Symmetry 259