Page 264 - Ganit Kaushal

Ex 10. Consider the capital letters of the English alphabet (A to Z). List the letters which have:

(a) a vertical line of symmetry (b) only a vertical line of symmetry
(c) a horizontal line of symmetry (d) only a horizontal line of symmetry

(e) no line of symmetry (f) both horizontal and vertical lines of symmetry
(g) both linear and rotational symmetry (h) rotational symmetry but no linear symmetry
Sol. (a) Vertical line of symmetry: A, H, I, M, O, T, U, V, W, X, Y.

(b) Only a vertical line of symmetry: A, M, T, U, V, W, Y.
(c) Horizontal line of symmetry: B, C, D, E, H, I, K, O, X.

(d) Only a horizontal line of symmetry: B, C, D, E, K.
(e) Having no line of symmetry: F, G, J, L, N, P, Q, R, S, Z.
(f) Having both horizontal and vertical lines of symmetry: H, I, O, X.

(g) Having both linear as well as rotational symmetry: H, I, O, X.
(h) Having rotational symmetry but no linear symmetry: N, S, Z.

Ex 11. How many lines of symmetry and angles of symmetry does this wheel with 12
spokes have? What is the least angle of symmetry?
Sol. The circular wheel has 12 spokes that make 6 diameters, and each diameter of a
circle is a line of symmetry.
\ Number of lines of symmetry = 6.

Because all spokes are at equal angles, it can be easily observed that this wheel
can be rotated 12 times to overlap itself to complete one full turn.
So, least angle of symmetry = 360° ÷ 12 = 30° and angles of symmetry = 30°, 60°, 30°
90°, 120°, 150°, 180°, 210°, 240°, 270°, 300°, 330°, 360°.

\ Total number of angles of symmetry = 12.

Miscellaneous Exercise 9.3

There are four options (Q. 1 to Q. 5), out of which only one is correct. Choose the correct option.
1. The letter which has both reflection and rotational symmetry is

(a) M (b) H (c) Y (d) S
2. Among the following symbols, the one having the maximum number of lines of symmetry is
(a) (b) (c) (d)

3. The number of lines of symmetry in a kite is
(a) 0 (b) 2 (c) 3 (d) 1
4. The total number of lines of symmetry in a scalene triangle is

(a) 0 (b) 2 (c) 3 (d) 1
5. Which of the following has an infinite number of lines of symmetry?
(a) wheel (b) alphabet ‘O’ (c) square (d) circle

262 Mathematics-6