The order of rotational symmetry of a regular pentagon is 5.
Understanding Rotational Symmetry
Rotational symmetry is a property of a shape when it looks the same after being rotated by a partial turn. The order of rotational symmetry is the number of times the shape looks identical to its original position during a full 360-degree rotation.
For a shape to have rotational symmetry of order greater than 1, it must be able to rotate onto itself at least once before completing a full circle.
Rotational Symmetry of a Regular Pentagon
According to the provided information, a regular pentagon has rotational symmetry of order 5. This means that as you rotate a regular pentagon around its center, it will align perfectly with its original position 5 times within a complete 360-degree turn.
- Reference Information: A regular pentagon has 5 rotational lines of symmetry, which means it has rotational symmetry of order 5.
This characteristic is inherent to all regular polygons. The order of rotational symmetry is equal to the number of sides of the regular polygon.
Why Order 5?
A regular pentagon has five equal sides and five equal interior angles. When you rotate it:
- After a rotation of 72° (360° / 5 sides), each vertex moves to the position previously occupied by the adjacent vertex, and the pentagon looks exactly the same.
- This happens a second time after another 72° rotation (total 144°).
- A third time after 216°.
- A fourth time after 288°.
- The fifth time is upon completing the full 360° rotation, bringing it back to the absolute starting position.
Since it matches its original appearance 5 times during the full rotation (including the starting/ending position), its order of rotational symmetry is 5.
| Shape | Type | Number of Sides | Order of Rotational Symmetry |
|---|---|---|---|
| Pentagon | Regular | 5 | 5 |
| Equilateral Triangle | Regular | 3 | 3 |
| Square | Regular | 4 | 4 |
| Hexagon | Regular | 6 | 6 |
Understanding the order of rotational symmetry is key in various fields like geometry, art, and design. For regular polygons, it provides a simple and direct relationship between the number of sides and this symmetry property.
