如图,在正方形ABCD中,点E,F在对角线BD上,且BE＝EF＝FD,连接AE,AF,CE,CF

（1）∵四边形ABCD是正方形,
∴AD = CD,∠ADF =∠CDF．
在△ADF和△CDF中,
∵AD = CD,∠ADF =∠CDF,DF = DF,
∴△ADF≌△CDF
∴AF = CF
（2）联结AC,AC与BD相较于点O．
∵四边形ABCD是正方形,
∴AC⊥BD,OA = OC,OB = OD
∵BE = EF = FD,OE = OB – BE,OF = OD – FD,
∴OE = OF
于是,由AC⊥BD,OA = OC,OE = OF,
得四边形AECF是菱形