Show two parrallelograms have same area

[DEMJR]

This is a proposition from Euclid that I want to prove (see attachment). AD and EF lie on a line parallel to BC. I want to show that Area of ABCD = Area of BCFE. I believe to prove this I must first show that triangle ABE is congruent to triangle DCF (then show that triangle GBC = triangle GED).

I know how to show that all the corresponding angles are the same for both triangles. I just do not know how to prove that the corresponding sides are congruent. Could you give me a clue on how to think about or begin showing that AB = DC or AE = EF or BE = CF? Thanks a bunch.

 

[tiny-tim]

Hi DEMJR!

… Could you give me a clue on how to think about or begin showing that AB = DC

But they're parallel lines cutting parallel lines (ie a parallelogram) …

they're almost trivially equal ​