Diagonals of Polygons

A diagonal of a polygon is a segment that connects any two vertices of the polygon that are not consecutive.

So, a square has 2 diagonals, a triangle has 0, etc.

If a polygon has n sides, we find that it has $\frac{n(n-3)}{2}$ diagonals.

Proof: There are $\binom{n}{2}$ segments connecting two vertices. Of these, n of them connect consecutive vertices, so we get $\binom{n}{2}-n=\frac{n(n-3)}{2}$ diagonals.