## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 14 Symmetry Objective Type Questions

**Mental Maths**

Question 1.

Fill in the blanks:

(i) The hands of a clock rotate only in ………. direction.

(ii) While opening the cap of a bottle, the direction of rotation is ……….

(iii) The number of lines of symmetry of an isosceles right-angled triangle is …………

(iv) A figure has ……….. symmetry if it is its own image under a reflection.

(v) The centre of rotation of an equilateral triangle is the point of intersection of its ………..

(vi) The centre of rotation of a rhombus is the point ……….

(vii) A regular polygon of n-sides has ……….. the number of lines of symmetry.

(viii) The angle of rotational symmetry in an equilateral triangle is ……….

(ix) The angle of rotational symmetry in a regular pentagon is ……..

(x) If after a rotation of 45° about a fixed point the figure looks exactly the same, then the order of rotational symmetry is ……….

Solution:

Question 2.

State whether the following statements are true (T) or false (F):

(i) The letter A has line symmetry but no rotational symmetry.

(ii) A rhombus is also a parallelogram and hence it does not have line symmetry.

(iii) A parallelogram has two lines of symmetry.

(iv) The order of rotational symmetry of a rhombus is four.

(v) A circle has exactly four lines of symmetry.

(vi) In a regular pentagon, the perpendicular bisector of the sides are the only lines of symmetry.

(vii) In a regular hexagon, the perpendicular bisector of the sides are the only lines of symmetry.

(viii) In a rectangle, the angle of rotational symmetry is 90°.

(ix) A semicircle has rotational symmetry of order 2.

(x) An isosceles triangle has neither a line symmetry nor a rotational symmetry.

(xi) If a figure possesses a rotational symmetry, then it must look exactly the same at least once up to a rotation of 180°.

(xii) The angle of rotation of a figure is obtained by dividing 360° by the order of rotational symmetry.

(xiii) A regular triangle has 3 lines of symmetry and rotational symmetry of order 3.

(xiv) A regular pentagon has 5 lines of symmetry and rotational symmetry of order 5.

Solution:

**Multiple Choice Questions**

Choose the correct answer from the given four options (3 to 14):

Question 3.

A quadrilateral having four lines of symmetry is a

(a) parallelogram

(b) rectangle

(c) rhombus

(d) square

Solution:

Question 4.

The letter Z has

(a) one horizontal line of symmetry

(b) one vertical line of symmetry

(c) two lines of symmetry

(d) no line of symmetry

Solution:

Question 5.

A figure that does not have any rotational symmetry is

(a) circle

(b) parallelogram

(c) kite

(d) regular pentagon

Solution:

Question 6.

The number of lines of symmetry in the given figure is

(a) 1

(b) 3

(c) 6

(d) infinitely many

Solution:

Question 7.

Rotating a figure by 60° anticlockwise is equivalent to a clockwise rotation of

(a) 60°

(b) 120°

(c) 240°

(d) 300°

Solution:

Question 8.

A figure having 1 line of symmetry and whose order of rotational symmetry is also 1 is

(a) rhombus

(b) parallelogram

(c) kite

(d) scalene triangle

Solution:

Question 9.

The order of rotational symmetry of a line segment is

(a) 1

(b) 2

(c) 3

(d) 4

Solution:

Question 10.

The order of the rotational symmetry in the given figure is

(a) 1

(b) 2

(c) 4

(d) infinitely many

Solution:

Question 11.

A possible angle of rotation of a figure having rotational symmetry of order greater than 1 is

(a) 36°

(b) 144°

(c) 150°

(d) 360°

Solution:

Question 12.

The figure which does not have both reflection and rotational symmetry is

Solution:

Question 13.

In the word ’MATHS’ which of the following pairs of letters have rotational symmetry?

(a) M and T

(b) A and S

(c) T and S

(d) H and S

Solution:

Question 14.

The letter which has both reflection and rotational symmetry is

(a) H

(b) M

(c) S

(d) Y

Solution: