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Toggle## Class 7, Maths, Chapter 14, Exercise 14.1 Solutions

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

**Ans: **Equilateral triangle, square and Circle.

**Q.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.**

**Ans:**

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

A triangle with both line and rotational symmetries of order more than 1 is an equilateral triangle.

** **

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

A triangle with only line symmetry and no rotational symmetry of order more than 1 is isosceles triangle.

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

it is not possible to draw because, a quadrilateral with a line symmetry may have rotational symmetry of order one but not more than one.

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

A quadrilateral with line symmetry but not a rotational symmetry of order more than 1 is trapezium.

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

**Ans:** Yes, because every line through the centre forms a line of symmetry, then it will have rotational symmetry for every angle.

**Q.4. Fill in the blanks:**

** Ans:**

**Q.5. Name the quadrilaterals which have both line and rotational symmetry of order more than 1.**

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

**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?**

**Ans: **The other angles are, 120°, 180°, 240°, 300°, 360°

**Q.7. Can we have a rotational symmetry of order more than 1 whose angle of rotation is (i) 45°? (ii) 17°?**

**Ans:**

**(i) 45°?**

Yes. We can have a rotational symmetry of order more than 1 whose angle of rotation is 45^{o} and rotations are 8.

**(ii) 17°?**

No. If the angle of rotational is 17°, then symmetry of order is not possible because 360° is not complete divided by 17°.