**Symmetry**

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

**Solution:-**

Equilateral triangle and Circle.

**2. Draw, wherever possible, a rough sketch of**

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

**Solution:-**

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

**Line symmetry**

**Rotational symmetry**

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

**Solution:-**

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.**

**Solution:-**

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

**Solution:-**

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

**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 have rotational symmetry of order more than 1.

**4. Fill in the blanks:**

Shape | Centre of Rotation | Order of Rotation | Angle of Rotation |

Square | |||

Rectangle | |||

Rhombus | |||

Equilateral Triangle | |||

Regular Hexagon | |||

Circle | |||

Semi-circle |

**Solution:-**

Shape | Centre of Rotation | Order of Rotation | Angle of Rotation |

Square | Intersecting point of diagonals | 4 | 90^{o} |

Rectangle | Intersecting point of diagonals | 2 | 180^{o} |

Rhombus | Intersecting point of diagonals | 2 | 180^{o} |

Equilateral Triangle | Intersecting point of medians | 3 | 120^{o} |

Regular Hexagon | Intersecting point of diagonals | 6 | 60^{o} |

Circle | Centre | Infinite | Every angle |

Semi-circle | Mid-point of diameter | 1 | 360^{o} |

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

**Solution:-**

The quadrilateral which have both line and rotational symmetry of order more than 1 is square.

Line symmetry:

Rotational symmetry:

**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:-**

The other angles are, 120°, 180°, 240°, 300°, 360°

So, the figure is said to have rotational symmetry about same angle as the first one. Hence, the figure will look exactly the same when rotated by 60° from the last position.

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

**(i) 45°?**

**Solution:-**

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

**(ii) 17°?**

**Solution:-**

No. We cannot have a rotational symmetry of order more than 1 whose angle of rotation is 17^{o}.