How many distinct diagonals of a convex heptagon (7-sided polygon) can be drawn?
I need to find a way to count the number of diagonals without drawing them all and risking double-counting. A diagonal is a line segment that connects two non-adjacent vertices of a polygon. So for each vertex, I can draw diagonals to all the other vertices except the two adjacent ones and itself. That means for each vertex, there are 7 - 3 = 4 possible diagonals. But wait, this counts each diagonal twice, once for each endpoint. So I need to divide by 2 to get the actual number of distinct diagonals. Therefore, the total number of diagonals is 7 * 4 / 2 = 14. 