Question

如图,AB‖CD, ∠EAF=1/4∠EAB, ∠ECF=1/4∠ECD.求证：∠AFC=3/4∠

如图,AB‖CD, ∠EAF=1/4∠EAB, ∠ECF=1/4∠ECD.求证：∠AFC=3/4∠AEC

Answer 1

证明：
如图作EG‖AB‖CD‖FH
∠AFC=∠AFH+∠CFH
=∠BAF+∠DCF
=3/4∠BAE+3/4∠DCE （∠EAF=1/4∠EAB, ∠ECF=1/4∠ECD）
=3/4(∠BAE+∠DCE)
=3/4(∠AEG+∠CEG)
=3/4∠AEC
证毕