Geometry Problem 481: Triangle, Altitude, Cevian, Perpendicular, Angle

The figure shows a triangle ABC with the altitude AF and a cevian BD. Line AE is perpendicular to BD extended, and BG is perpendicular to line EF extended. Prove that angles ABD and CBG are congruent.
A cevian is a segment which joins a vertex of a triangle with a point on the opposite side (or its extension).