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Let us perform half turns about the centre of the rhombus marked.

A P C A P

D B 180° D 360°
B D B

C A P C
(i) (ii) (iii)
In the figure above fig (i) is the initial position. Rotation by 180° about
the centre leads to fig (ii). Observe the position of point P.
Quick Check
Rotate again through 180° and we get fig (iii). Thus, when we complete
two half turns, the rhombus reaches it original position. It looks same What is the order of
as in fig (iii). rotational symmetry
of isosceles triangle?
Thus, the rhombus has a rotational symmetry of order 2 about its
centre with an angle of rotation of 180°.
Example 3: Discuss the rotational symmetry of an equilateral triangle.

Solution:
A

120°
120°
120° A
A
(i) (ii) (iii)

In the figure above, fig (i) is the initial position. Rotation through 120° about the centre leads to
fig (ii). Observe the position of point A.

Again, rotate through 120°, and we get fig (iii). It looks the same as fig (i). We can see with the help
of the positions taken by A.

Thus, the equilateral triangle has a rotational symmetry of order 3 about its centre with an angle
of rotation 120°.

Example 4: State whether the figure shows rotational symmetry or not. Find the
order of rotational symmetry.

Solution: Yes, the given figure shows the rotational symmetry.

Initial position 90° 180° 270° 360°
Clearly, the order of symmetry = 4 (90°, 180°, 270° and 360°).

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