### NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Ex 14.3

**Ex 14.1 Class 7 Maths Question 1.**

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

**Solution:**

English alphabet H and O both have line symmetry and rotational symmetry.

**Ex 14.3 Class 7 Maths 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) Equilateral triangle has 3 rotational symmetries.

(ii) Not possible.

(iii)

(iv) Not possible.

**Ex 14.3 Class 7 Maths Question 3.**

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

**Solution:**

Yes. The above figure has two lines of symmetry and also rotational symmetry of order 2.

**Ex 14.3 Class 7 Maths Question 4.**

**Fill in the blanks:**

Shape | Centre of rotation | Order of rotation | Angle of rotation |

Square | |||

Rectangle | |||

Rhombus | |||

Equilateral triangle | |||

Regular hexagon | |||

Circle | |||

Semicircle |

**Solution:**

Shape | Centre of rotation | Order of rotation | Angle of rotation |

Square | Point of intersection of diagonals | 4 | 90° |

Rectangle | Point of intersection of diagonals | 4 | 90° |

Rhombus | Point of intersection of diagonals | 4 | 90° |

Equilateral triangle | Point of intersection of medians | 3 | 120° |

Regular hexagon | Point of intersection of diagonals | 6 | 60° |

Circle | Centre | Infinite | Every angle |

Semicircle | Centre | 4 | 90° |

**Ex 14.3 Class 7 Maths Question 5.**

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

**Solution:**

Square, rectangles and rhombus are such quadrilateral which have both line and rotational symmetry.

**Ex 14.3 Class 7 Maths 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:**

If a figure is rotated through the angles 120°, 180°, 240°, 300° and 360°, it looks exactly the same.

**Ex 14.3 Class 7 Maths Question 7.
**

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

**(i) 45°?**

**(ii) 17°?**

**Solution:
**(i) Yes

(ii) No