Question

如图,已知A、B、C、D在一条直线上,AB=CD,EB⊥AD,FC⊥AD,AE=DF.求证：AF=DE

Answer 1

因为：AB=CD AE=DF EB⊥AD FC⊥AD

所以：BE=CF

因为：EB⊥AD FC⊥AD BE=CF

所以：EF//BC

因为：BE=CF AB=CD AE=DF EB⊥AD FC⊥AD

所以：∠AEB=∠DFC

因为：EF//BC EB⊥AD FC⊥AD∠AEB=∠DFC

所以：∠AEF=∠DFE

因为：∠AEF=∠DFE EF=EF AE=FD

所以：AF=DE