Class 7 Maths Symmetry Rotational Symmetry

Rotational Symmetry

When an object rotates, its shape and size do not change. The rotation turns an object about a fixed Point known as centre of rotation. The angle of turning during rotation is called the angle of rotation. A full turn  means a rotation of 360°. A half-turn means rotation by 180° and a quarter-turn is rotation by 90°.

A shape or object has Rotational Symmetry when it still looks the same after some rotation.

Example: A paper windmill is a perfect example of symmetry. In a paper windmill, there is no line of symmetry, neither can it be folded. Paper windmill shows rotational symmetry. It is fixed to a stick by a pin.

The angle at which this paper mill is turned is called the angle of rotation. Here the angle of turn is 90°. A full turn of rotation measures 360°. So for taking one full turn, our paper windmill is moved four times.

So, it has a rotational symmetry of order 4.

Again, a square has a rotational symmetry of order 4. The centre of rotation is the centre of the square and the angle of rotation is 90°.

Problem: Which of the following figures have rotational symmetry of order more than 1:

Solution:

Rotational symmetry of order more than 1 are (a), (b), (c), (d), (e) and (f) because in these figures, a

complete turn, more than 1 number of times, an object looks exactly the same.

Problem: Name any two figures that have both line symmetry and rotational symmetry.

Solution:

Two figures that have both line symmetry and rotational symmetry are: Circle and Square.

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