已知A、F、C、D四點在同一條直線上,AC=DF,AB‖DE,EF‖BC,試說明:(1)△ABC≌△DEF;(2)∠CBF=∠FEC.

已知A、F、C、D四點在同一條直線上,AC=DF,AB‖DE,EF‖BC,試說明:(1)△ABC≌△DEF;(2)∠CBF=∠FEC.

證明:(1)∵AB‖DE,∴∠A=∠D,∵EF‖BC,∴∠EFD=∠BCA,在△ABC和△DEF中,∠A=∠DAC=DF∠EFD=∠BCA,∴△ABC≌△DEF(ASA);(2)∵△ABC≌△DEF,∴EF=BC∵EF‖BC,∴四邊形EFBC是平行四邊形,∴∠CBF=∠FEC.