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Convex and Concave Polygons

Every polygon is either *convex* or *concave.* The
difference between
convex and concave polygons lies in the measures of their
angles. For a polygon to be
convex, all of its
interior angles must be less than 180
degrees. Otherwise, the polygon is
concave.
Another way to think of it is this: the diagonals of a convex
polygon will
all be in the interior of the polygon, whereas certain diagonals of a concave
polygon will lie outside the polygon, on its exterior. Below in Part A are some
convex polygons, and in Part B, some concave polygons. In the rest of this
text, you can assume that every polygon discussed is convex.

Figure %: Convex and concave polygons

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Regular Polygons

Polygons can also be classified as equilateral, equiangular, or both.
Equilateral polygons have congruent sides,
like a rhombus. Equiangular polygons have congruent interior angles, like a
rectangle. When a polygon is both equilateral and equiangular, it is called
a regular polygon. A square is an example of a regular polygon. The
center of a regular polygon is the point
from which all the vertices of the polygon are equidistant. Regular
polygons have special properties that we'll explore in the next section. Below
are some examples of equiangular, equilateral, and regular polygons.

Figure %: Equilateral, equiangular, and regular polygons

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Congruent Polygons

One more note on polygons: Polygons whose sides are all congruent are
congruent polygons. Knowing this term will be important later. In
congruent polygons, every segment is
congruent.