Order of Rotational Symmetry

Definition of Order of Rotational Symmetry:

The number of times a figure fits into itself in one complete rotation is called the order of rotational symmetry.

If A° is the smallest angle by which a figure is rotated so that rotated from fits onto the original form, then the order of rotational symmetry is given by $\frac{360°}{A°}$, [A° < 180°]

Order of rotational symmetry = $\frac{360}{\textrm{Angle of Rotation}}$

A figure has a rotational symmetry of order 1, if it can come to its original position after full rotation or 360°.

Examples of Order of Rotational Symmetry:

Rectangle (clockwise)

$Order of Rotation$

We observe that while rotating the figure through 360°, it attains original from two times i.e., it looks exactly the same at two positions. Thus, we say that the rectangle has a rotational symmetry of order 2.

Equilateral triangle (clockwise):

$Order of Rotational Symmetry$

We observe that at all 3 positions, the triangle looks exactly the same when rotated about its center by 120°.

Letter B (clockwise):

$Definition of Order of Rotational Symmetry$

We observe that only at one position the letter looks exactly the same after taking one complete rotation.

Windmill (anticlockwise):

$anticlockwise$

We observe that if we rotate it by one – quarter, at 4 positions, it looks exactly the same. Therefore, the order of rotational symmetry is 4.

Solved Examples on Order of Rotational Symmetry:

1. Find the order of rotational symmetry of the following shapes about the point marked.

$Problems on Rotational Symmetry$

Solution:

(i)

$Problems on Order of Rotational Symmetry$

Order of rotational symmetry = $\frac{360}{180}$ = 2

(ii)

$Rotational Symmetry Problems$

Order of rotational symmetry = $\frac{360}{60}$ = 6

2. The figure obtained by giving 2 anticlockwise right-angle turns to letter G is:

$2 Anticlockwise Right-angle Turns$

Answer: (ii)

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