A point S is marked somewhere inside triangle PQR, and straight lines are drawn from S to each of the three corners P, Q and R. How many triangles are there in the finished drawing?

The three lines from S cut the big triangle into three small ones: PQS, QRS and RPS. Add the original triangle PQR itself and the total is 4. Nothing else is a triangle, because any other choice of three lines would need two of the segments from S plus a side, and those two segments together with a side already form one of the three small triangles counted. The trap is 3, from counting only the pieces the drawing has been cut into and forgetting that the outline PQR is still a triangle in its own right.