Question

In ÄABC shown below, point A is at (0, 0), point B is at (x2, 0), point C is at (x1, y1), point D is at x sub 1 over 2, y sub 1 over 2, and point E is at the quantity of x sub 1 plus x sub 2 over 2, y sub 1 over 2:

Triangle ABC is shown. Point D lies on segment AC and point E lies on segment BC. A segment is drawn between points D and E. Point A is at the origin.

Prove that segment DE is parallel to segment AB.