如图，点A,E,F,B在同一条直线上，AC⊥CE，BD⊥DF，AE=BF,AC=BD.求证：CE=DF.

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(1)∵ AC⊥CE, BD⊥DF∴∠ACE=∠BDF又∵AC=BD,AE=BF∴Rt△ACE≌Rt△BDF∴CE=DF(2)∵Rt△ACE≌Rt△BDF∴∠AEC=∠BFD即 ∠CEF=∠DFE∴CE∥DF