What is the rotational symmetry of a regular pentagon
The Correct Answer and Explanation is:
The rotational symmetry of a regular pentagon is 5.
Explanation:
Rotational symmetry refers to the number of times a shape can be rotated about a central point, within one full turn (360 degrees), and still look the same as it originally did. A regular pentagon is a polygon with five equal sides and five equal angles, making it symmetric in multiple ways.
To determine the rotational symmetry of a regular pentagon, we need to assess how many distinct positions it can take during a complete rotation of 360 degrees, where the shape looks exactly the same as the starting position. For a regular pentagon:
- First Rotation: If the pentagon is rotated by 72 degrees (360 degrees divided by 5), it will match its initial position.
- Second Rotation: Another rotation of 72 degrees (making 144 degrees in total) will also align the pentagon with its original appearance.
- Third Rotation: After a further 72 degrees (216 degrees total), the pentagon will still look the same.
- Fourth Rotation: After rotating another 72 degrees (288 degrees total), the pentagon will again be in the same orientation.
- Fifth Rotation: Finally, when rotated by 72 degrees once more (360 degrees in total), the pentagon returns to its original position.
Thus, a regular pentagon has five distinct positions where it can match its original shape in one full 360-degree rotation. These positions occur every 72 degrees, demonstrating that the regular pentagon has 5 lines of rotational symmetry.
The importance of rotational symmetry lies in its application in art, design, architecture, and nature, where symmetric patterns create balance and aesthetic harmony. The regular pentagon’s rotational symmetry ensures that it looks the same from multiple angles.
