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**NCERT solutions for Maths Symmetry ****Download as PDF**

## NCERT Solutions for Class 7 Maths Symmetry

**Class –VII Mathematics(Ex. 14.3)**

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

**Answer: **Circle and Square.

NCERT Solutions for Class 7 Maths Exercise 14.3

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

- a triangle with both line and rotational symmetries of order more than 1.
- a triangle with only line symmetry and no rotational symmetry of order more than 1.
- a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.
- a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.

**Answer:**(i) An equilateral triangle has both line and rotational symmetries of order more than 1.

Line symmetry:

Rotational symmetry:

(ii)An isosceles triangle has only one line of symmetry and no rotational symmetry of order more than 1.

Line symmetry:

Rotational symmetry:

(iii)It is not possible because order of rotational symmetry is more than 1 of a figure, most acertain the line of symmetry.

(iv)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:

NCERT Solutions for Class 7 Maths Exercise 14.3

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

**Answer: **Yes, because every line through the centre forms a line of symmetry and it has rotational symmetry around the centre for every angle.

NCERT Solutions for Class 7 Maths Exercise 14.3

**Question** 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 |

**Answer: **Sol.

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

Square | Intersecting point of diagonals. | 4 | {tex}{90^ \circ }{/tex} |

Rectangle | Intersecting point of diagonals. | 2 | {tex}{180^ \circ }{/tex} |

Rhombus | Intersecting point of diagonals. | 2 | {tex}{180^ \circ }{/tex} |

Equilateral triangle | Intersecting point of medians. | 3 | {tex}{120^ \circ }{/tex} |

Regular hexagon | Intersecting point of diagonals. | 6 | {tex}{60^ \circ }{/tex} |

Circle | Centre | infinite | At every point |

Semi-circle | Mid-point of diameter | 1 | {tex}{360^ \circ }{/tex} |

NCERT Solutions for Class 7 Maths Exercise 14.3

**Question** 5. Name the quadrilateral which has both line and rotational symmetry of order more than 1.

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

Line symmetry:

Rotational symmetry:

NCERT Solutions for Class 7 Maths Exercise 14.3

**Question** 6. After rotating by {tex}{60^ \circ }{/tex} about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

**Answer: **Other angles will be {tex}120^\circ ,180^\circ ,240^\circ ,300^\circ ,360^\circ {/tex}.

For rotation:It will rotate six times.

For rotation:It will rotate three times.

For rotation:It will rotate two times.

For rotation:It will rotate one time.

NCERT Solutions for Class 7 Maths Exercise 14.3

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

(i) {tex}{45^ \circ }{/tex}(ii) {tex}{17^ \circ }{/tex} ?

**Answer: **(i) If the angle of rotation is {tex}{45^ \circ },{/tex} then symmetry of order is possible and would be 8 rotations.

(ii) If the angle of rotational is {tex}{17^ \circ },{/tex} then symmetry of order is not possible because {tex}{360^ \circ }{/tex} is not complete divided by {tex}{17^ \circ }.{/tex}

## NCERT Solutions for Class 7 Maths Exercise 14.3

NCERT Solutions Class 7 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 7 Maths includes text book solutions from Class 7 Maths Book . NCERT Solutions for CBSE Class 7 Maths have total 15 chapters. 7 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 7 solutions PDF and Maths ncert class 7 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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Centre of rotation should be in number

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