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are congruent. Clearly, this is a special case of a triangle, because scalene triangles do not have this
property. Nor do obtuse triangles.

Question:

Which of the following figures must be equilateral and equiangular?

A Circle

B Triangle

C Square

D Hexagon

Answer

The correct answer is C because all of the sides and angles of a square are congruent. Choice A is
incorrect, because, as perfect as they are, circles have neither sides nor angles. Choices B and D are
incorrect. Both trangles and hexagons can have unequal sides and angles. For example, here’s a
hexagon that is neither equilateral nor equiangular:

Unusual hexagon

A regular polygon is a polygon that is both equilateral and equiangular.

What do you call a regular quadrilateral?

Yes, it’s a square! By the way, have you found a relationship between the number of sides, angles, and
vertices in a polygon? They are all equal. A triangle has three vertices, a pentagon has five sides, and a
decagon has ten angles.

Interior and Exterior Angles of Polygons

When you reviewed the definition of an angle earlier, you learned that an angle has an interior and an
exterior. So it shouldn’t surprise you that polygons, which are composed of angles, have interiors and
exteriors, as well.

An exterior angle of a polygon is the angle between one side of the polygon and the extension of an
adjacent side. ACB is an exterior angle of ACD.