BE平分∠ABC,
∠ABE=∠FBE=90°/2=45°；
AD//BC,∠AEB=∠FBE=45°；[内错角]
∠AEB=∠ABE=45°;AB=AE
EF⊥BC,EF//AB,∠BEF=∠ABE=45°；[内错角]
∠AEF=∠AEB+∠BEF=90°;
∠FBE=∠BEF=45°;BF=EF;
AB²+AE²=BE²=BF²+EF²
2AB²=2BF²
AB=BF
AB=AE=BF=EF.
∠A=∠ABF=∠EFB=∠AEF=90°;
所以四边形ABFE是正方形.