## MP Board Class 7th Maths Solutions Chapter 14 Symmetry Ex 14.3

Question 1.

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

Solution:

An equilateral triangle and regular hexagon have both line symmetry and rotational symmetry.

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.

Solution:

(i) An equilateral triangle has 3 lines of symmetry and rotational symmetry of order 3.

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

(iii) A parallelogram is a quadrilateral which has no line symmetry but a rotational symmetry of order 2.

(iv) A kite is a quadrilateral which has only 1 line of symmetry and no rotational- symmetry of order more than 1.

Question 3.

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

Solution:

Yes, if a figure has two or more lines of symmetry, then it will definitely have its rotational symmetry of order more than 1.

Question 4.

Fill in the blanks:

Solution:

The given table can be completed as follows:

Question 5.

Name the quadrilaterals which have both line and rotational symmetry of order more than 1.

Solution:

Square, rectangle, and rhombus are the quadrilaterals which have both line and rotational symmetry of order more than 1. A square has 4 lines of symmetry and rotational symmetry of order 4. A rectangle has 2 lines of symmetry and rotational symmetry of order 2. A rhombus has 2 lines of symmetry and rotational symmetry of order 2.

Question 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:

It can be observed that if a figure looks symmetrical on rotating by 60°, then it will also look symmetrical on rotating by 120°, 180°, 240°, 300°, 360° i.e., further multiples of 60°.

Question 7.

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

(i) 45°?

(ii) 17°?

Solution:

It can be observed that if the angle of rotation of a figure is a factor of 360°, then it will have a rotational symmetry of order more than 1.

(i) It can be checked that 45° is a factor of 360°. Therefore, the figure having its angle of rotation as 45° will have its rotational symmetry of order more than 1.

(ii) 17° is not a factor of 360°. Therefore, the figure having its angle of rotation as 17° will not be having its rotational symmetry of order more than 1.