A Florida roof company must check that each roof truss it sells is made of two congruent triangles.
Since we know ∠BAG ≈ ∠DEF, and AC ≈ EC, △ABG and △ACF, and △EDF and △ECG are similar triangles. This means the angles ∠ACF ≈ ∠ECG. All we need to know now is CF ≈ CG, which is your answer :)