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Symmetry

Identification of Figures that Show Rotational Symmetry and Finding their Order of Symmetry

We know that a square has four lines of symmetry as shown in the following figure. If we rotate the square about the point of intersection of its diagonals through an angle of 90° four times then an original figure will be obtained as shown in the following figure. Thus, we can say that a square has a rotational symmetry of order 4.

Now, let us look at the following figure of an equilateral triangle. An equilateral triangle has three lines of symmetry. If we rotate the triangle about the centre of rotation through an angle of 120° then a similar shape will be obtained. Here, we have to rotate the triangle through 120° three times to take the triangle to its original position. Therefore, the equilateral triangle is said to have a rotational symmetry of order 3, about the centre of rotation.

From the above examples, we can observe that

If a figure has more than one line of symmetry then it has rotational symmetry of order equal to the number of its lines of symmetry”.

What happens when the lines of symmetry do not exist? Can we say anything about the figure then?

Consider the figure of a fan with four blades. It does not have any line of symmetry but still it has rotational symmetry of order 4. If we rotate the fan about its centre through an angle of 90°, then a similar shape will be obtained. We have to rotate the fan through 90° fourtimes to take the fan to its original position. Therefore, the fan is said to have a rotational symmetry of order 4, about the centre of rotation.

Thus, we can say that

When the lines of symmetry do not exist for a figure, the figure can …

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