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Question

What are the rotational symmetry orders of the following: Parallelogram, Rectangle, Square, Rhombus, Kite, and Trapezium? (Note: Trapezium, not Trapezoid)


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Solution

Order of the rotational symmetry.

The number of positions in which a figure may be rotated and yet appear precisely as it did before the revolution is known as the order of symmetry.

Parallelogram: After a 180° spin, the parallelogram transforms into itself. As a result, it possesses two rotational symmetry orders.

Rectangle: After a 180° spin, the rectangle transforms into itself. As a result, it possesses two rotational symmetry orders.

Square: After a 90° spin, the square transforms into itself. As a result, it has four rotational symmetry orders.

Rhombus: After a 180°spin, the rhombus transforms into itself. As a result, it possesses two rotational symmetry orders.

Kite: After a 360° spin, the rectangle transforms into itself. As a result, it possesses one rotational symmetry order.

Trapezium: After a 360° spin, the trapezium transforms into itself. As a result, it possesses one rotational symmetry order.


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