In the figure below, A, G, B, F, and C are collinear; DB is perpendicular to BE; DG is perpendicular to AC; and EF is perpendicular to AC. If DB is 20 units long, EB is 10 units long, and EF is 8 units long, how many units long is DG?

I know that the answer is 12 but I'm having trouble justifying why the triangle are similiar, I just don't see the proof of it :(