A polygon is a closed shape whose boundaries consist of straight lines. A shape if convex if, for any two points that are part of the shape, a straight line can not be drawn between the two points that lies outside the shape.^{[1]}

Figure 1 is an example of a concave polygon. Since it is possible to pick two points within the shape and draw a line between them that leaves the shape, the shape is convex.  

Figure 2 is an example of a convex polygon. Note that the entire line is contained within the polygon. In fact, a line drawn between any two points that are part of the' polygon will be entirely contained within the polygon. 
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