A diagonal of a polygon is a line that connects two non-adjacent vertices. (See Figure 5.29.) How many diagonals are there in a triangle? A quadrilateral? A pentagon? Formulate a conjecture for the...

A diagonal of a polygon is a line that connects two non-adjacent vertices. (See Figure 5.29.) How many diagonals are there in a triangle? A quadrilateral? A pentagon? Formulate a conjecture for the number d(k) of diagonals in a k-gon, and prove your formula correct by induction. (Hint: consider lopping off a triangle from the polygon.)