How many unique diagonals can be drawn in a five-sided convex polygon?
I need to find a way to count the number of diagonals in a pentagon without actually drawing them all. A diagonal is a line segment that connects two non-adjacent vertices of a polygon. So, for each vertex of the pentagon, I can draw two diagonals: one to the vertex that is two steps clockwise, and one to the vertex that is two steps counter-clockwise. That means I can draw 10 diagonals in total, but some of them are repeated. For example, the diagonal from A to C is the same as the one from C to A. So, I need to divide the total number of diagonals by 2 to get the number of unique ones. Therefore, the answer is 10/2 = 5. 