# Ncert Solutions For Class 7 Maths Ex 14.3

## Ncert Solutions For Class 7 Maths Chapter 14 Ex 14.3

Q.1. Name any two figures that have both line symmetry and rotational symmetry.

Solution: Circle and Square.

Q.2. Draw, wherever possible, a rough sketch of:

(a)A triangle with both line and rotational symmetries of order more than 1.

(b)A triangle with only line symmetry and no rotational symmetry of order more than 1.

(c)A quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.

(d)A quadrilateral with line symmetry but not a rotational symmetry of order more than 1.

Solution:

(a)An equilateral triangle has both line and rotational symmetries of order more than 1.

Line symmetry:

Rotational symmetry:

(b) An isosceles triangle has only one line of symmetry and no rotational symmetry of order more than 1.

Line symmetry:

Rotational symmetry:

(c) It is not possible because order of rotational symmetry is more than 1.

(d) A trapezium, which has equal non-parallel sides, a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.

Line symmetry:

Rotational symmetry:

Q.3. In a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?

Solution: Yes, because every line through the centre forms a line of symmetry and it has rotational symmetry around the centre for every angle.

Q.4. Fill in the blanks:

Solution:

Q.5. Name the quadrilateral that has both line and rotational symmetry of order more than 1.

Solution: Square has both line and rotational symmetry of order more than 1.

Line symmetry:

Rotational symmetry:

Q.6. After rotating by 60 about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

Solution: Other angles will be . 120,180,240,300,360$120^{\circ},180^{\circ},240^{\circ},300^{\circ},360^{\circ}$

For 60$60^{\circ}$ rotation: It will rotate six times.

For 120$120^{\circ}$  rotation: It will rotate three times.

For 180$180^{\circ}$rotation: It will rotate two times.

For 360$360^{\circ}$rotation: It will rotate one time.

Q.7. Can we have a rotational symmetry of order more than 1 whose angle of rotation is:

(i) 45$45 ^{\circ}$

(ii) 17$17^{\circ}$

Solution:

(i)If the angle of rotation is 45$45 ^{\circ}$  , then symmetry of order is possible and would be 8 rotations.

(ii)If the angle of rotational is 17$17^{\circ}$ , then symmetry of order is not possible because 360$360^{\circ}$ is not complete divided by 17$17^{\circ}$ .