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# Definitions

A polygon is a collection of coplanar segments that intersect only at their endpoints and where each endpoint is shared by exactly two segments. The segments are called sides; each endpoint is a vertex. A segment that connects to non-adjacent vertices is called a diagonal. Diagonals in most polygons are relatively uninteresting. The diagonals of a quadrilateral, however, can have some interesting properties.

A regular polygon is a polygon where all of the sides are congruent.

A convex polygon is a polygon where any two points inside the polygon can be connected by a segment that never leaves the polygon. A concave polygon is a polygon where there are pairs of points inside the polygon that cannot be connected by a segment that never leaves the polygon.

 Example Polygon Convex Concave Regular Comments No N/A N/A N/A This isn't a polygon because vertex A is an endpoint for three segments. The definition says there can be only two. No N/A N/A N/A This isn't a polygon because vertex A is an endpoint for none of the segments. The definition says that the segments are only allowed to intersect at their endpoints. Yes No Yes Yes This polygon is concave because there are points inside the figure (e.g. A and B) where the segment connecting them passes outside the polygon. The polygon is regular becaues all the sides have the same length. Yes Yes No No This polygon is convex because there are no points inside the figure where the segment connecting them passes outside the polygon. The polygon is not regular becaues all of the sides do not have the same length. No N/A N/A N/A This isn't a polygon because two of the segments don't meet. The definition says that each endpoint must be shared by exactly two segments.

## Named Polygons

Polygons are 'named' based on the number of sides they have. An n-sided polygon is called an n-gon. In other words, a 15-sided polygon would be called a 15-gon. Some polygons, ones with a relatively small number of sides, have special names. For reference: all of the examples below are regular, convex polygons.

 Name Sides Example triangle 3 hexagon 6 nonagon 9
 Name Sides Example quadrilateral 4 heptagon 7 decagon 10
 Name Sides Example pentagon 5 octagon 8