Consider the following polygon with 10 vertices such that $H,G,F,I$ are colinear:
Note that it is known that any triangulation of a polygon with $n$ vertices gives has $n-2$ triangles. In the figure above, we have 10 vertices but only 6 triangles. Is this a valid triangulation? Or perhaps I is it possible that I cannot take $\triangle JHI$ as a single triangle since that would mean intersecting with the original polygon too many times (it also intersects with $G$ and $F$)?
Any triangle in a triangulation must have exactly 3 vertices. (I'm answering this under community wiki so the question can be marked as answered.)