NCERT Solutions for Class 8 Maths - Symmetry- 2

Exercise 14.3 

Question 1: 

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

Answer 1: 

Circle and Square.

Question 2: 

Draw, wherever possible, a rough sketch of: 

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

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

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

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

Answer 2: 

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

Line symmetry:

Rotational symmetry:

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

Line symmetry:

Rotational symmetry:

(iii) A quadrilateral with no line of symmetry is an irregular quadrilateral

Checking rotational symmetry
If it is rotated 90°

It does not looks same as initial figure
If it is rotated 180°

It does not looks same as initial figure
If it is rotated 360°

It looks same as initial figure
Thus,

Thus, order of rotational symmetry - 1
Hence,
A quadrilateral with a rotational symmetry of order not a line of symmetry Is not possible

(iv) 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: 

Question 3: 

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

Answer 3: 

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

Question 4: 

Fill in the blanks: 

Answer 4: 

Question 5: 

Name the quadrilateral which has both line and rotational symmetry of order more than 1. 

Answer 5: 

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

Line symmetry:  

Rotational symmetry:

Question 6: 

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

Answer 6: 

Other angles will be 120°, 180°,240°,300°,360°.

For 60° rotation:

It will rotate six times.

For 120° rotation:

It will rotate three times.

For 180° rotation:

It will rotate two times.

For 360° rotation:

It will rotate one time.

Question 7: 

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

(i) 45^o 
(ii) 17^o ? 

Answer 7: 

(i) If tiie angle of rotation is 45°, then symmetry of order is possible and would be 8 rotations.
(ii) If the angle of rotational is 17°, then symmetry o f order is not possible because 360° is not complete divided by 17°.