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

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The figure below shows right triangles ABC and A₁B₁C₁ so that medians BM and B₁M₁ are parallel. BA and B₁A₁ meet at D, BC and C₁B₁ meet at E, and C₁A₁ and AC meet at G. If F is on the extension of C₁E, prove that angle ADA₁ = angle CEF = half the measure of angle CGC₁.

Infographic Geometry problem 1128 Right Triangles, Medians, Parallel, Angles, Congruence, Half the measure