A line parallel to the base cuts a triangle into a small triangle and a trapezium, and both diagonals of the trapezium are drawn. How many triangles are there?

Sort by inner lines used. None: 1. One: the parallel line gives 1, each diagonal gives 2, so 5. Two: 5 (3 from the two diagonals, 1 each with the parallel line). Three: the triangle between the parallel line and the crossing point, 1. Total $1+5+5+1=12$.