Question

已知：如图,AB＜BC,BD是∠ABC的平分线,EF平行BC,求证：∠DEC=∠FEC

Answer 1

在BC上取一点E,使得：BE = AB .

因为,在△ABD和△EBD中,AB = EB ,∠ABD = ∠EBD ,BD为公共边,

所以,△ABD ≌ △EBD ,

可得：∠A = ∠BED ,AD = ED ；

因为,ED = AD = CD ,可得：∠C = ∠CED ；

所以,∠A+∠C = ∠BED+∠CED = 180° .