Online Geometry Problem 609: Triangle, Perpendiculars, 90 Degrees, Collinearity. Level: Mathematics Education, High School, College

The figure shows a triangle ABC with a point D. DE is perpendicular to DC (E is on BA extended), DF is perpendicular to DA (F is on BC extended), and DG is perpendicular to DB (G is on AC extended). Prove that points E, F, G are collinear.