Types of Symmetry

There are two types of Symmetry

1. Reflection Symmetry

If we draw a dotted line which gives the mirror reflection of the other half of the image then it is reflection symmetry. It is the same as basic symmetry which tells us that if the dotted line divides the image into two equal halves then it is the reflective symmetry of the figure.

2. Rotational Symmetry

If we rotate the image at a centre point of the image at 360° then the number of times the image looks the same, shows the rotational symmetry of the image.

Rotational Symmetry

  • If a figure rotates at a fixed point then that point is the centre of Rotation.
  • It could rotate clockwise or anticlockwise.
  • While rotation the measurement of the angle which we take is the angle of rotation. And a complete rotation is of 360°.
  • If the angle of rotation is 180° then it is called Half Turn and if the angle of rotation is 90° then it is called a Quarter Turn.

This image looks symmetrical but there is no line of symmetry in it i.e. there is any such line which divides it into two equal halves. But if we rotate it at 90° about its centre then it will look exactly the same. This shows that it has Rotational Symmetry.

While rotating, there are four positions when the image looks exactly the same. So this windmill has a rotational symmetry of order 4 about its centre.

Example

What is the Rotational symmetry of the given figure?

Solution:

To find the rotational symmetry, we have to find

  • The angle of rotation = 90°
  • Direction = clockwise
  • Order of rotation = 4

This shows that if the given figure rotates anticlockwise at 90° around its centre then it has rotational symmetry of order 4.

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