Final answer:
Polygons with sides of equal length and angles of equal measure are called regular polygons. They vary in shape depending on the number of sides and maintain uniformity in their geometric properties.
Step-by-step explanation:
Polygons whose sides all have the same length and whose angles all have the same measure are known as regular polygons. A regular polygon not only looks uniform in appearance, but also balances equally in terms of its geometric properties. For example, a square is a regular polygon with four sides of equal length and four angles of equal measure, each being 90 degrees. This class of polygons can vary in shape based on the number of sides they have, but each retains uniformity in sides and angles. This distinguishes them from irregular polygons, where the lengths of the sides and the measures of the angles differ. It's also important to note that regular polygons are always convex, meaning all interior angles are less than 180 degrees, and no sides curve inward.