A regular polygon is a polygon that is both equilateral and equiangular, meaning all its sides have the same length and all its interior angles are equal in measure
. Regular polygons can be convex or star-shaped (concave), but in all cases, their vertices lie on a common circumscribed circle, making them cyclic polygons
. Key properties of regular polygons include:
- Equal side lengths and equal interior angles.
- The sum of the exterior angles is always 360°.
- They have rotational symmetry of order equal to the number of sides.
- They have an inscribed circle (incircle) tangent to each side at its midpoint
Examples of regular polygons are:
- Equilateral triangle (3 sides)
- Square (4 sides)
- Regular hexagon (6 sides)
In summary, a regular polygon is a highly symmetrical polygon with all sides and angles equal, often used as fundamental shapes in geometry
