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what is a concave polygon?

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A polygon is a closed plane curve made up of straight line segments.  If the curve is not self-intersecting, that is none of the line segments cross each other then it is a convex polygon or a concave polygon.  The way to tell the difference is that if you pick any two points in the polygon or on the boundary lines, and connect them with a straight line, the straight line may or may not go outside the polygon.  If it stays inside between the points the polygon is convex, if it intersects the boundary and goes outside the polygon then the polygon is concave.
Simply speaking, if you have a convex polygon, no diagonal drawn will intersect any of the polygon's sides except at the vertices.
If you have a concave polygon, you can draw one or more diagonals that will intersect one or more of the polygon's sides at points other than the vertices.
Hey Jacob,
 
To answer your question a convex polygon is the ones that you generally are acquainted with. The definition for a convex polygon is really that it is not a concave polygon...I know this seems unhelpful but by definition a concave polygon is a polygon whose internal angle is greater than 180 degrees. Therefore a convex polygon has to have an internal angles which are NOT greater than 180 degrees.
 
consider the convex polygons you should know. A stop sign which is an octagon does not have internal angles which are greater than 180 degrees, just like a triangle, square, rectangle, pentagon and so forth. These have a nice formula which can be described by (n-2) x 180 degrees / n where n stands for the number of sides. This is the case with all convex polygons, but NOT concave, since those follow different rules.