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

问题描述:

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

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