证明：∵在RtΔABC中，AD⊥BC∴∠BAD＝∠ACB＝∠F∵E是AC的中点∴DE＝EC∴∠EDC＝∠ECD＝∠BDF＝∠F∴BD＝ BF∴∠BDF＝∠BAD∵∠F＝∠F∴ΔADF∽ΔBDFBD／AD＝DF／AF∵RtΔBDA∽RtΔBAC∴BD／AD＝AB／AC∴DF／AF＝AB／AC∴AB·AF＝AC·DF
