Which type of polygon has all sides congruent?

A polygon is defined as a closed figure made up of a finite number of line segments, which are called sides. In geometry, a regular polygon is characterized by having all sides of equal length and all angles of equal measure. This property of congruence in both sides and angles makes regular polygons a specific subset of polygons.

For instance, all sides of an equilateral triangle are the same length, as are all sides of a square, making both regular polygons. This congruence is crucial in various geometric calculations, such as finding the area or determining the symmetry of the shape.

Irregular polygons, on the other hand, have sides and angles that are not congruent, meaning their side lengths and angle measures can vary. Convex polygons have all interior angles less than 180 degrees and vertices that point outward, but this does not ensure that all sides are of equal length. Concave polygons have at least one interior angle greater than 180 degrees and one vertex that points inward, again not requiring equal side lengths.

The definition of a regular polygon confirms that it is precisely this type of shape that has all sides congruent, making the selection of this answer the most appropriate choice.