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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

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

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.

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