∵∠BAC=∠BEC=90°，∠ADB=∠CDE，∴∠ABD=∠ACF，又∵AB=AC，∠BAD=∠FAC=90°，∴△ABD≌△ACF，∴BD=FC，∠ABD=∠FCA，故①②正确；又∵BE为△BCF的角平分线，BE⊥CF，∴△EBF≌△EBC∴EF=EC，故④正确．正确个数为3，故选B．
