Theshapes and objects that look the same after a certain amount of rotation aresaid to have rotational symmetry. Some shapes look the same after half a turn.If we turn English alphabet S around a centre point by 180° we get the alphabetS in the same position. The angle of turning during a rotation is called theangle of rotation. A complete turn means 360°, so a half turn means 180° and aquarter turn means 90°.

You are watching: What rotation symmetry does a square have

This rotation can be: (a) clockwise (b) anticlockwise

The fixed about which the figure is rotated is called centre of rotation.

The angle of turning during rotation is called the angle of rotation.

A quarter turn means a rotation of 90°

A half turn means a rotation of 180°

A full turn means a rotation of 360°

A figure is said to have rotational symmetry if it onto more than once during a complete rotation, i.e., 360°

Take a square piece and draw lines, as shown in the figure.Place a pin in the centre where the lines meet. Now, rotate this square by 90°about its centre. The square looks exactly the same. In a full turn 360° thereare 4 positions when the square looks exactly the same.


Thus, a square has a rotational symmetry of order 4 aboutits centre of rotation. Hence, the angle of rotation is 90°.

Order of rotational symmetry = (frac360 extrmAngle of Rotation)

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

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● Related Concepts

Linear Symmetry

Lines of Symmetry

Point Symmetry

Order of Rotational Symmetry

Types of Symmetry


Reflection of a Point in x-axis

Reflection of a Point in y-axis

Reflection of a point in origin


90 Degree Clockwise Rotation

90 Degree Anticlockwise Rotation

180 Degree Rotation

7th Grade Math Problems8th Grade Math PracticeFrom Rotational Symmetry to HOME PAGE

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