What Is a Polygon With All of Its Sides and Angles Congruent?

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An angle with all of its sides and angles congruent is a regular polygon. The term "congruent" means exactly equal in shape or size, while a polygon is defined as a closed figure made up of sides that are line segments.

Every square, by definition, has four sides of equal length and four right angles measuring 90 degrees each. Because the sides and angles are congruent, a square also classifies as a regular polygon.

An equilateral triangle is considered a regular polygon because it has three congruent sides and three angles measuring 60 degrees each. The right triangle is not a regular polygon because it has one 90-degree angle and two smaller angles that add up to 90 degrees. In an isosceles right triangle, these two smaller angles both measure 45 degrees each. In a 30-60-90 triangle, one of the smaller angles measures 30 degrees and the other measures 60 degrees.