# Is every triangle a quadrilateral?

I can imagine a quadrilateral where one of the angles is $180^\circ$. Is this still considered a quadrilateral?

More generally, is every $n$-gon also a $(n+1)$-gon (for $n \ge 3$)?

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An $\aleph_1$-gon? ;) – Rex Oct 26 '12 at 0:06
If the $n$-gons are allowed to flex (like a planar linkage) it is better to allow degenerate cases with two or more consecutive sides collinear to count as having $n$ sides, because these will be intermediate positions in a motion between convex and concave positions of the linkage. Else you are forced into odd phrases like the flexing polygon having $n$ sides at times $t < t_0$ and instantaneously transforming into an $(n-1)$-gon at time $t_0$ before changing back to its $n$-gonal self at times $t > t_0$.