The diagonal through vertex A 1 and the diagonal through vertex A3, and the diagonal through vertex A 1 and the diagonal through vertex A4 all overlap. Induction: Starting from a vertex of a polygon, (n-3) diagonals can be drawn. N vertices * * * have n(n-3) diagonals, but half of them are repeated, so the number of diagonals of an n polygon is n(n-3)/2.

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