Page 263 - Ganit Kaushal

Ex 6. State whether the following statements are True (T) or False (F).

(a) The line of symmetry divides the shape into two identical parts.
(b) Angles of symmetry are multiples of the least angle of symmetry.
(c) The letter A has linear symmetry but no rotational symmetry.

(d) In a regular pentagon, the perpendicular bisectors of the sides are the only lines of symmetry.
(e) In a regular hexagon, the perpendicular bisectors of the sides are the only lines of symmetry.
(f) A circle has 4 lines of symmetry.

Sol. (a) True (b) True (c) True (d) True
(e) False [ Lines passing through vertices are also lines of symmetry.]
(f) False [ It has infinitely many lines of symmetry.]

Ex 7. Fill in the blanks.
(a) A line of symmetry is also known as a _______ line or _______ of symmetry.
(b) The number of capital letters of the English alphabet having only a vertical line of symmetry is
_______.
(c) The number of capital letters of the English alphabet having only a horizontal line of symmetry is
_______.

(d) The number of capital letters of the English alphabet having both horizontal and vertical lines of
symmetry is _______.

(e) A regular polygon of ‘n’ sides has _______ lines of symmetry.
Sol. (a) mirror, axis (b) 7 (c) 5 (d) 4

(e) n
Subjective/Competency Based Questions
Ex 8. Find the number of lines of symmetry (if any) and draw them for each of the following shapes:

(a) (b) (c)

Sol. (a) (b) (c)

(only 1 line (3 lines of (4 lines of
of symmetry) symmetry) symmetry)
Ex 9. Give two examples of figures that have one line of symmetry but do
not have rotational symmetry.
Sol. A trapezium with equal base angles and a half circle have one line of
symmetry as shown in alongside figures. They have only one angle Trapezium Half circle
of symmetry and that is 360°. So, they do not have rotational symmetry.

Symmetry 261