Question

如图,在Rt△ACB中,∠ACB=90°,CD⊥AB,AF平分∠CAB,AF平分∠CAB,求证∠CEF=∠CFE

Answer 1

∠CFE=∠FAB+∠B=∠A/2+∠B

∠AED=∠FAC+∠ACD

Rt△ACB中,∠ACB=90°

得到∠A+∠B=90°

CD⊥AB,得到∠A+∠ACD=90°

∠ACD=∠B

∠AED=∠FAC+∠ACD=∠A/2+∠B=∠CFE

∠AED=∠CEF

所以∠CEF=∠CFE