Page 260 - Ganit Kaushal

(b) It can be easily observed that this figure overlaps itself after a quarter-turn for the first time.

\ Least angle of symmetry = 90° and angles of symmetry = 90°, 180°, 270°, 360°
( Angles of symmetry are multiples of the least angle of symmetry)

Order of rotational symmetry = 360° ÷ 90° = 4.
(c) This figure has six arms.
\ Least angle of symmetry = 360° ÷ 6 = 60° and angles of symmetry = 60°, 120°, 180°, 240°,
300°, 360°.

Order of rotational symmetry = 360° ÷ 60° = 6.
Ex 6. Draw two figures other than a circle and a square that have both reflection symmetry and rotational
symmetry. (NCERT)

Note

Sol. (a) (b) Students are advised to explore some
different kinds of figures having both reflection
symmetry and rotational symmetry.

Ex 7. Draw, wherever possible, a rough sketch of (NCERT)

(a) A triangle with at least two lines of symmetry and at least two angles of symmetry.
(b) A triangle with only one line of symmetry but not having rotational symmetry.

(c) A quadrilateral with rotational symmetry but no reflection symmetry.
(d) A quadrilateral with reflection symmetry but not having rotational symmetry.
(e) A shape with two lines of symmetry and two angles of symmetry.

Sol. (a) Any equilateral triangle will work (see figure (i)).
Number of lines of symmetry = 3

Angles of symmetry = 120°, 240°, 360°.
(b) Any isosceles triangle will work (see figure (ii)).
Number of lines of symmetry = 1 Fig. (i): Equilateral triangle Fig. (ii): Isosceles triangle

Angle of symmetry = 360° (No rotational symmetry)
(c) Any parallelogram will work (see figure (iii)).
Number of lines of symmetry = 0 (No reflection symmetry)

Angles of symmetry = 180 °, 360° Fig. (iii): Parallelogram
(d) Any trapezoid with equal angles at the base will work (see figure (iv)).
Number of lines of symmetry = 1 (vertical, as shown in the figure)

Angle of symmetry = 360° (No rotational symmetry) Fig. (iv): Trapezoid
(e) The given adjacent shape will work (see figure (v)).

Number of lines of symmetry = 2 (dotted lines)
Angles of symmetry = 180 °, 360°.
(Students are advised to explore some other shapes in all these cases.)
Fig. (v)

258 Mathematics-6