Page 259 - Ganit Kaushal

Ex 2. Which of the following figures has more than one angle of
symmetry? Write the angles of symmetry, least angles of
symmetry and order for those shapes. (NCERT)
Sol. Figure (a): It has 4 angles of symmetry because there are 4 (a) (b) (c)
spokes present in the wheel.
\ Least angle of symmetry = 360° ÷ 4 = 90°; Angles of symmetry = 90°, 180°, 270°, 360°
( Angles of symmetry are multiples of the least angle of symmetry);
Order = 360° ÷ 90° = 4.
Figure (b): It can be easily observed that it does not have more than one angle of symmetry.
Figure (c): It has 3 angles of symmetry because there are 3 spokes present in the wheel.
Least angle of symmetry = 360° ÷ 3 = 120°; Angles of symmetry = 120°, 240°, 360°

( Angles of symmetry are multiples of the least angle of symmetry);
Order = 360° ÷ 120° = 3.
Ex 3. Draw a figure with radial arms that has (a) exactly 5 angles of symmetry, (b) exactly 6 angles of
symmetry. Also, find the angles of symmetry in each case. (NCERT)

Sol. We know that: Number of radial arms = Number of angles of symmetry
(a) There are five radial arms in figure (i).
\ Least angle of symmetry = 360° ÷ 5 = 72°. 72° 60°
Angles of symmetry = 72°, 144°, 216°, 288°, 360°.
( Angles of symmetry are multiples of the least angle
of symmetry)
(b) There are six radial arms in figure (ii).
\ Least angle of symmetry = 360° ÷ 6 = 60°. (i) (ii)
Angles of symmetry = 60°, 120°, 180°, 240°, 300°, 360°.
( Angles of symmetry are multiples of the least angle of Note
symmetry) Students may think of some
Ex 4. Check whether the following statements are True or False: other kinds of figures.
(a) Every figure will have 360° as an angle of symmetry.

(b) If the least angle of symmetry of a figure is a natural number in degrees, then it is a factor of 360.
(c) A circle has an infinite number of lines of symmetry as well as angles of symmetry.
(d) All angles of symmetry are multiples of the least angle of symmetry.
(e) A shape can have both angles of symmetry as well as lines of symmetry.
Sol. (a) True (b) True (c) True (d) True
(e) True
Ex 5. Give the angles of symmetry and order of rotational symmetry for each figure: (NCERT)

(a) (b) (c)

Sol. (a) It can be easily observed that this figure overlaps itself after a half-turn for the first time.
\ Least angle of symmetry = 180° and angles of symmetry = 180°, 360°
Order of rotational symmetry = 360° ÷ 180° = 2.

Symmetry 257