NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

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

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

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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?

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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:

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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?

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

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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
(h) A quadrilateral
(i) A regular hexagon
(j) A circle

Answer :

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

Answer :

(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.

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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?

Answer :

(a) median
(b) Diameter