A parallelogram can always be decomposed into two identical triangles by a segment that connects opposite vertices.

Going the other way around, two identical copies of a triangle can always be arranged to form a parallelogram, regardless of the type of triangle being used. To produce a parallelogram, we can join a triangle and its copy along any of the three sides that match, so the same pair of triangles can make different parallelograms. Here are examples of how two copies of both Triangle A and Triangle F can be composed into three different parallelograms.

This special relationship between triangles and parallelograms can help us reason about the area of any triangle.