Page 262 - Ganit Kaushal

2. Which of the following figures has more than one angle of symmetry? Write the angles of symmetry,
the least angle of symmetry and the order for those shapes.

(a) (b) (c) (d)

3. Draw a figure with radial arms having exactly 7 angles of symmetry. What will be its smallest angle
of symmetry? Is the number of degrees a whole number in this case? If not, express it as a mixed
fraction. (NCERT)

4. Give the angles of symmetry and order of rotational symmetry for each given figure. (NCERT)

(a) (b) (c)

5. Find the lines of symmetry, the least angle of symmetry, the angles of symmetry
and the order for the given rangoli picture. How many times does it overlap itself
in taking a full turn of 360 degrees?

6. If 40° is the least angle of symmetry, what are the other angles of symmetry in this figure?
7. 90° is an angle of symmetry. The figure has two angles of symmetry less than 90°. What is the least
angle of symmetry?
8. Can we have a figure with rotational symmetry whose least angle of symmetry is 17°?

Miscellaneous Solved Examples

There are four options (Q. 1 to Q. 5), out of which only one is correct. Choose the correct option.

Ex 1. An equilateral triangle is symmetrical about each of its
(a) altitudes (b) medians (c) angle bisectors (d) all of them

Sol. (d) since, in an equilateral triangle, altitudes, medians, and angle bisectors are the same.
Ex 2. The number of lines of symmetry of an N-sided regular polygon is
(a) N (b) 2N (c) 3N (d) 4N
Sol. (a)

Ex 3. If a figure has rotational symmetry, then its least angle of symmetry is
(a) < 360° (b) > 180° (c) ≤ 180° (d) None of these
Sol. (c)

Ex 4. In the word ‘MATHS’, which of the following pairs of letters have rotational symmetry?
(a) M and A (b) H and S (c) T and A (d) S and A
Sol. (b)
Ex 5. A possible least angle of symmetry for a figure having rotational symmetry of order greater than 1 is

(a) 144° (b) 150° (c) 210° (d) 36°
Sol. (d) since, 36 divides 360.

260 Mathematics-6