Geometry Problem 1128:
Right Triangles, Medians, Parallel, Angles, Congruence,
Half the measure. Level: High School, SAT Prep,
Honors Geometry, College, Math Education

The figure below shows right
triangles ABC and A_{1}B_{1}C_{1} so that medians BM and B_{1}M_{1} are
parallel. BA and B_{1}A_{1} meet at D, BC and C_{1}B_{1} meet at E, and C_{1}A_{1}
and AC meet at G. If F is on the extension of C_{1}E, prove that angle ADA_{1} = angle CEF = half the
measure of angle CGC_{1}.