如图,AB平分CD,∠ABC=∠ADC,AE=CF,BE=DF,求证：EF与AC互相平分

图呢?图∵AB∥CD∴∠BAC=∠DCA 又AC=AC∠ABC=∠ADC ∴⊿ABC≌⊿CDA∴AB=CD∵AE=CFBE=DF∴⊿AEF≌⊿CFD∴∠EAB=∠FCD∴∠EAC+∠BAC=∠FCD+∠DCA即∠EAC=∠FCA∴AE∥CF又AE=CF∴四边形AECF是平行四边形∴EF与AC互相平分