*According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 12.
NCERT Solutions for Class 7 Maths Exercise 14.3 Chapter 14 Symmetry in simple PDF are available here. Students are advised to check the solutions for each question present in this exercise and resolve the difficulties faced while solving the problems from the NCERT Class 7 books. This exercise of NCERT Solutions for Maths Class 7 Chapter 14 contains topics related to Line symmetry and Rotational symmetry.
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Access Answers to NCERT Solutions for Class 7 Maths Chapter 14 – Symmetry Exercise 14.3
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 an 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 a 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 | 90o |
| Rectangle | Intersecting point of diagonals | 2 | 180o |
| Rhombus | Intersecting point of diagonals | 2 | 180o |
| Equilateral Triangle | Intersecting point of medians | 3 | 120o |
| Regular Hexagon | Intersecting point of diagonals | 6 | 60o |
| Circle | Centre | Infinite | Every angle |
| Semi-circle | Mid-point of diameter | 1 | 360o |
5. Name the quadrilaterals which have both line and rotational symmetry of order more than 1.
Solution:-
The quadrilateral, which has both line and rotational symmetry of order more than 1, is a 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 the 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 45o.
(ii) 17°?
Solution:-
No. We cannot have a rotational symmetry of order more than 1 whose angle of rotation is 17o.
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