# NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

Written by Team Trustudies
Updated at 2021-02-11

## NCERT solutions for class 7 Maths Chapter 14 Symmetry Exercise 14.1

Q.1 Copy the figures with punched holes and find the axes of symmetry for the following:

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

Q.2 Give the line(s) of symmetry, find the other hole(s):

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

Q.3 In the following figures, the mirror line (i.e., the line of symmetry) is given as a dotted line. Complete each figure performing reflection in the dotted (mirror) line. (You might perhaps place a mirror along the dotted line and look into the mirror for the image). Are you able to recall the name of the figure you complete?

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

Q.4 The following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry.
Identify multiple lines of symmetry, if any, in each of the following figures:

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

Here, figure (a),(b), (c) , (d), (e), (g) and (h) are the multiple lines of symmetry.

Q.5 Take any one diagonal as a line of symmetry and shade a few more squares to make the figure symmetric about a diagonal. Is there more than one way to do that? Will the figure be symmetric about both the diagonals?

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

Q.6 Copy the diagram and complete each shape to be symmetric about the mirror line(s).

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

Q.7 State the number of lines of symmetry for the following figures:
(?) An equilateral triangle
(b) An isosceles triangle
(c) A scalene triangle
(d) A square
(e) A rectangle
(f) A rhombus
(g) A parallelogram
(i) A regular hexagon
(j) A circle

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

(a) An equilateral triangle$?$ 3
(6) An isosceles triangle $?$ 1
(c) A scalene triangle $?$ 0
(d) A square $?$ 4
(e) A rectangle $?$ 2
(f) A rhombus $?$ 2
(g) A parallelogram $?$ 0
(h) A quadrilateral $?$ 0
(i) A regular hexagon $?$ 6
(j) A circle $?$ Infinite

Q. 8 What letters of the English alphabet have reflectional symmetry (i.e., symmetry related to mirror reflection) about.
(a) a vertical mirror
(b) a horizontal mirror
(c) both horizontal and vertical mirrors

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

(a) Alphabet of vertical mirror reflection symmetry are
A, H, I, M, O, T, U, V, W, X, Y
(b) Alphabet of horizontal mirror reflection symmetry are:
B, C, D, E, H, I, K, O, X
(c) Alphabet of both horizontal and vertical mirror reflection symmetry are:
H, I, O, X.

Q.9 Give three examples of shapes with no line of symmetry.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

A scalene triangle, our palm and a parallelogram

Q.10 What other name can you give of the line of symmetry of
(a) an isosceles triangle?
(b) a circle?

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

(a) median
(b) Diameter

## NCERT solutions for class 7 Maths Chapter 14 Symmetry Exercise 14.2

Q.1 Which of the following figures have rational symmetry of order more than 1:

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

The figure (a), (b), (d), (e) and (f) have rotational symmetry more than 1.

Q.2 Give the order of rotational symmetry for each figure:

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

(a) Order of rotational symmetry = 360°/180°=2

(b) Order of rotational symmetry = 360°/180°=2

(C) Order of rotational symmetry = 360°/120°=3

(d) Order of rotational symmetry = 360°/90°=4

(e)Order of rotational symmetry = 360°/90°=4

(f) Order of rotational symmetry = 360°/72°=5

(g) Order of rotational symmetry = 360°/60°=5

(h) Order of rotational symmetry = 360°/120°=3

## NCERT solutions for class 7 Maths Chapter 14 Symmetry Exercise 14.3

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

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

Equilateral triangle and square

Q.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.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

(i) Equilateral triangle has 3 rotational symmetries.

(ii) 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 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 is rhombus.

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

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

Yes. If a figure has two or more lines of symmetry, then it will have rotational symmetry of order more than 1.

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

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

Square, rectangles and rhombus

Q.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?

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

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

Q.7 Can we have a rotational symmetry of order more than 1 whose angle of rotation is
(i) 45°?
(ii) 17°?

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry