∵AB=AE AC=AD∠EAC=∠DAB(直角加公共角)∴△AEC≌△ABD(SAS)∴∠ACE=∠ADB∵∠ADC+∠ACD=90°∴∠ADB+∠BDC+∠DCA=90°∴∠ACE+∠BDC+∠DCA=90°即∠FCD+∠FDC=90°∴∠DFC=90°∴BD⊥CE