如图,在四边形ABCD中,AE平分∠BAD,CF平分∠BCD,∠BAD与∠DCB互补,∠DFC与∠DCF互余,说明AE∥CF
问题描述：
如图,在四边形ABCD中,AE平分∠BAD,CF平分∠BCD,∠BAD与∠DCB互补,∠DFC与∠DCF互余,说明AE∥CF
答
∵ ,DFC与∠DCF互余
故∠DFC+∠DCF=90°
∵∠BAD与∠DCB互补
故∠BAD+∠DCB=180 °
∴ ∠ADC=∠ABC=90°
故 ∠BCF+∠DAE=1/2(∠BAD+∠DCB)=90°
又 ∠BAE+∠AEB=∠DAE+∠AEB=90°
∴ ∠BCF=∠AEB
∴ AE//CF