# Symmetry

## Exercise 14.1

Question 1.
Copy the figures with punched holes and find the axis of symmetry for the following:

Solution:
The axis of symmetry is shown by following line.

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

Solution:

Question 3.
In the following figures, the mirror line (i.e., the line of symmetry) is given as 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?

Solution:
Following are the complete figures.

Question 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:

Solution:
Here, figure (6), (d), (e), (g) and (h) are the multiple lines of symmetry.

Question 5.
Copy the figure given here.
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?

Solution:
(i) Let us take a diagonal as the axis of symmetry and shade the square as shown in the figure.

(ii) Yes, there are more than the line of symmetry i.e. BD, EF and GH.
(iii) Yes, the figure is symmetric about both the diagonals.

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

Solution:

Question 7.
State the number of lines of symmetry for the following figures:
(а) 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
Solution:

Figure Number of lines of 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
(i) A regular hexagon  = 6
(j) A circle    =  Infinite

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

Question 9.
Give three examples of shapes with no line of symmetry.
Solution:
Example 1: Scalene triangle has no line of symmetry.
Example 2: Quadrilateral has no line of symmetry.
Example 3: Alphabet R has no line of symmetry.

Question 10.
What other name can you give of the line of symmetry of
(a) an isosceles triangle?
(b) a circle?
Solution:
(a) Median of an isosceles triangle is its line of symmetry.
(b) Diameter of a circle is its line of symmetry.

## Exercise 14.2

Question 1.
Which of the following figures have rotational symmetry of order more than 1?

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

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

Solution:

Let us take a point S on one end of the given figure. Rotating by 180°, S comes at other end and then again rotating by 180°, it comes at its original position.

∴ Order of rotational symmetry = 360/180 = 2

Let us take any point S in figure (1). It takes two rotations to come back to its original position.
∴ Order of rotational symmetry = 360/180 = 2

Let us mark any vertex of the given figure. It takes three rotations to come back to its original shape.
∴ Order of rotational symmetry = 360/120 = 3

Order of rotational symmetry = 360/90 =4

∴ Order of rotational symmetry = 360/90 = 4

(f) The given figure is a regular pentagon which can take one rotation at an angle of 72°.
∴ Order of rotational symmetry = 360/72 = 5

(g) The given figure requires six rotations each through an angle of 60°
∴ Order of rotational symmetry = 360/60 = 6

(h) The given figure requires three rotations, each through an angle of 120°.
∴ Order of rotational symmetry = 360/120 = 3