证明：∵∠ACE+∠EAC=90° ∠ACE+∠BCF =90°∴∠EAC=∠BCF 在Rt△AEC和Rt△CFB中∵AC=BC∠EAC=∠BCF ∠AEC=∠BFC=90°∴RT△AEC≌RT△CFB（ASA）∴CE=BFAE=CF=EF+CE又∵CE=BF∴AE=BF+EF
