A trapezium has one rotational symmetry order.
Understanding Rotational Symmetry
Rotational symmetry describes how many times a shape looks the same as you rotate it around its center point, before completing a full 360-degree turn. The order of rotational symmetry is the number of positions in which the rotated shape appears identical to the original.
For instance, a square has rotational symmetry order 4 because it looks the same after rotations of 90°, 180°, 270°, and 360°.
Rotational Symmetry of a Trapezium
A standard trapezium (or trapezoid) is a quadrilateral with at least one pair of parallel sides. Unlike shapes like squares, circles, or regular polygons, a trapezium typically does not have the property of looking identical after being rotated by angles less than 360 degrees.
As stated in the reference: "After a spin, the trapezium transforms into itself. As a result, it possesses one rotational symmetry order."
This means the only rotation that makes a trapezium look exactly the same as its original position is a full 360-degree rotation.
Why Order 1?
Consider a typical trapezium with one pair of parallel sides of different lengths and non-parallel sides of different lengths. If you rotate this shape by 90°, 180°, or 270°, its orientation changes, and it will not coincide with its starting position. Only a complete 360° rotation brings it back to the original appearance.
Rotational Symmetry Orders of Common Shapes
To illustrate, here's a simple comparison:
| Shape | Rotational Symmetry Order |
|---|---|
| Trapezium | 1 |
| Rectangle | 2 |
| Square | 4 |
| Equilateral Triangle | 3 |
| Circle | Infinite |
Even an isosceles trapezium, which has line symmetry (a mirror image), still only has rotational symmetry of order 1. It takes a full 360-degree turn for it to appear identical to its starting position when rotated about its center.
In conclusion, the rotational symmetry of a trapezium is order 1.
