convex and concave polygon

[shahar]

1. How can I prove that polygons are divided only to convex and concave polygon?
2. What about cases of degenerate polygon like: degenerate square, degenerate triangle, degenerate parallelogram?

 

[lookagain]

1. How can I prove that polygons are divided only to convex and concave polygon?

There are also self-intersecting polygons.

 

[Dr.Peterson]

It depends on exactly how you define "polygon". Different authors, in different contexts, allow different special situations. Some disallow self-intersecting polygons, some disallow degenerate cases where successive vertices are collinear; while others allow them.

I don't know what a degenerate square could be; a degenerate triangle would be a line segment, as would a degenerate parallelogram. If you allow them to be called polygons, then you'd have to check your definition of convex to see if it fit.

Many people are not aware how much variation there can be in definitions. Here is something I wrote about that (with a link to more).

So if you want help with a proof, show us the definitions you are using for "polygon", "convex", and "concave".