Question

如图,在△ABC中,∠C=2∠B,AD为△ABC的角平分线,求证：AB=AC+CD

Answer 1

在AB上取一点E,使得：AE = AC .

在△AED和△ACD中,AE = AC ,∠DAE = ∠DAC ,AD为公共边,

所以,△AED ≌ △ACD ,

可得：∠AED = ∠C ,ED = CD .

因为,∠BDE = ∠AED-∠B = ∠C-∠B = ∠B ,

所以,EB = ED = CD ；

可得：AB = AE+EB = AC+CD .