In the figure, three lines fan out from the top of a triangle, and a single line cuts across parallel to the…

Explanation

1. 01

   From the top vertex there are 5 lines in all: the two sides and the 3 inner lines. Any 2 of them form a triangle with a horizontal line as the third side.

2. 02

   Pairs of lines from the vertex: $\binom{5}{2} = 10$.

3. 03

   Horizontal lines that can close them: 2 (the base and 1 parallel line).

4. 04

   Triangles $= 10 \times 2 = 20$.