证明：
∵等边△ABC
∴∠BAC＝∠ABC＝∠ACB＝60
∵∠DEF＝∠CBE+∠BCF,∠CBE＝∠ACF
∴∠DEF＝∠ACF+∠BCF＝∠ACB＝60
∵∠DFE＝∠ACF+∠CAD,∠ACF＝∠BAD
∴∠DFE＝∠BAD+∠CAD＝∠BAC＝60
∴∠EDF＝180-∠DEF-∠DFE＝60
∴∠DEF＝∠DFE＝∠EDF＝60
∴等边△DEF