A rectangle has one diagonal from its top-left corner, and a line from its top-right corner to the middle of the bottom side. How many triangles are there?

The diagonal makes 2 halves. The second line meets the diagonal at P and gives 4 more: one on the top side, one on the bottom side, and two that have the right side as a side (one with its third corner at P, one at the middle of the base). Total $2+4=6$.