Question

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

Answer 1

（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