Let ∠E=X

∠∠A = 3∠E

∴∠A=3X

∵Rt△ABC, d is the midpoint of AB.

∴CD= 1/2AB,AD=CD

∴∠A=∠ACD=3X

∵Rt△EFC, g is the midpoint of EF.

∴CG= 1/2EF,CG=EG

∴∠E=∠ECG=X

∠∠CGD =∠E+∠ ECG, ∠ CDG =∠ ACD-∠ E.

∴∠CGD=X+X=2X,∠CDG=3X-X=2X

∴∠CGD=∠CDG

∴CG=CD

∫CD = 1/2AB，CG= 1/2EF

∴AB=EF

I hope it helps you!