*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 .

For

For

For

For

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

*(i) 45∘ *

*(ii) 17∘*

**Solution: **

(i)If the angle of rotation is

(ii)If the angle of rotational is