Question

在四边形ABCD中,AB=DA,AD=BC,∠ADC的平分线交CB的延长线于F,∠ABC的平分线交AD的延长线于E.求证

Answer 1

∵AB=DC,AD=BC,∴四边形ABCD是平行四边形,

∴AE‖CF,有∠ADF=∠DFC,∠CBE=∠AEB,

又∵DF平分∠ADC,EB平分∠ABC,

∴∠ADF=∠CDF,∠CBE=∠ABE,

∴∠AEB=∠ABE,∠CDF=∠CFD

即CD=CF,AB=AE

又∵AB=CD,

∴CF=AE,

∵AD=BC,∴AE-AD=CF-BC

即DE=BF