Two lines go from the bottom-left corner of a triangle to the right side, and one line from the bottom-right corner to the left side. How many triangles are there?

Sort by inner lines used. None: 1. One: each inner line splits the triangle in 2, so 6. Two: the two lines from the same corner give 1; each of them with the third line gives 3, so 7. Three: 1. Total $1+6+7+1=15$.