A common example of rotational symmetry in math is a rectangle.
Understanding Rotational Symmetry with a Rectangle
Rotational symmetry occurs when a shape or object looks exactly the same after being rotated a certain number of degrees around a central point.
The Rectangle Example
Based on the provided reference:
- A rectangle is a specific example of a shape that exhibits rotational symmetry.
- When you rotate a rectangle by 180 degrees around its geometric center, it appears identical to its original position and orientation.
- This means the rectangle has rotational symmetry of order 2, as there are two positions within a full 360-degree rotation where it looks the same (the original position and after a 180-degree rotation).
Other Shapes with Rotational Symmetry
While a rectangle is a clear example, many other shapes also possess rotational symmetry to varying degrees.
- Square: Has rotational symmetry of order 4 (rotates onto itself every 90 degrees).
- Equilateral Triangle: Has rotational symmetry of order 3 (rotates onto itself every 120 degrees).
- Circle: Has infinite rotational symmetry, as it looks the same after rotation by any angle.
These examples help illustrate how different shapes behave when rotated around a central point.
| Shape | Angle of Rotation | Order of Symmetry |
|---|---|---|
| Rectangle | 180° | 2 |
| Square | 90° | 4 |
| Equilateral Triangle | 120° | 3 |
Understanding rotational symmetry is a fundamental concept in geometry, helping to classify shapes based on their properties under rotation.
