Thread: convex quadrilateral, trisected.

Hello, the question I am stuck on is this one "Go Geometry: Elearn Geometry Problem 150" and I've seen a few answers stating "[BAH]=[BHG]=[BGD]". Under what proof does this statement work? i know they have two sides which are the same but how does that prove they are congruent. And even after that how does it help to find out if that sections area is one third of the whole area.
Please help.
Thanks in advance

I've attached a generalization to the problem. For the specific trisection problem, take c1=1/3 and c2=2/3. I hope it's understandable.