∵AB=BC,∴∠A=∠C,由旋转可得:∠A'=∠C'=∠A=∠C,旋转角∠ABA'=∠CBC',BA'=BC'=BA=BC,∴△ABE≌△C'BF,∴BE=BF,∴A'B-BE=BC-BF,即A'E=FC