Which figure has rotational symmetry

A regular pentagon has 5 sides and 5 lines of symmetry. The number of lines of symmetry in a regular polygon is equal to the number of sides. A shape has rotational symmetry when it can be rotated and it still looks the same. The order of rotational symmetry of a shape is the number of times it can be rotated around a full circle and still look the same. It only has one order of rotational symmetry, the starting position.

Thus, a square has a rotational symmetry of order 4 about its centre of rotation. We will learn how to use nets to find the surface area of a solid? Let us take a box made of cardboard. If we cut open the box and flatten it out, the flat shape is called the net of the box. A net is a two-dimensional shape that can be folded to make a three-dimensional. The number of times a figure fits into itself in one complete rotation is called the order of rotational symmetry.

We know that any object or shape which can be cut in two equal halves in such a way that both the parts are exactly the same is called symmetrical and the line which divides the shape in two equal halves is called the line of symmetry. A shape can have many lines of symmetry. If we place a mirror on the line of symmetry we can see the complete image. So, we find that the mirror image or reflection of the image in the mirror and the given figure are exactly symmetrical.

This type of symmetry is called reflection symmetry. The arrow you see below has a rotational symmetry of order 1. You do not need to do 90 degrees rotation each time. You can rotate a figure any amount of degrees you like to see if you will get the original figure. In our example above, we rotated a rectangle 90 degrees each time. Notice that we were able to get the original shape twice.

The first time we got the original image, we got it with a rotation of degrees and the second time, we got it with a rotation of degrees. Since we were able to return the original shape 2 times, the rectangle has rotational symmetry of order 2. In this last example above, we rotated a hexagon 60 degrees each time.

Each 60 degrees rotation returns the original shape as you can see above. Since we were able to return the original shape 6 times, the hexagon has rotational symmetry of order 6.

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