如圖,AD∥BC,∠A=∠C,BE、DF分別平分∠ABC和∠CDA.求證:BE∥DF.

如圖,AD∥BC,∠A=∠C,BE、DF分別平分∠ABC和∠CDA.求證:BE∥DF.

證明:∵AD∥BC,∴∠A+∠ABC=180°,∠C+∠ADC=180°,∵∠A=∠C,∴∠ABC=∠ADC,∵BE、DF分別平分∠ABC和∠CDA,∴∠EBC=12∠ABC,∠EDF=12∠ADC,∴∠EBC=∠EDF,∵AD∥BC,∴∠DFC=∠EDF,∴∠EBC=∠DFC,∴BE∥DF.