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

**NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Exercise 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