Q:

What is a polygon with all of its sides and angles congruent?

A:

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.

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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.

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