In △ ABC, the angle ABC = 90, ad is the angular bisector, the points E F are on AC ad, and AE = AB EF / / BC prove that bdef is a diamond

In △ ABC, the angle ABC = 90, ad is the angular bisector, the points E F are on AC ad, and AE = AB EF / / BC prove that bdef is a diamond

∵∠BAF=∠EAF AB=AE AF=AF
∴△ABF ≌△AEF
∴BF=EF ∠AFB=∠AFE
∴∠BFD=∠EFD
∵EF//BC
∴∠EFD=∠BDF
∴∠BFD=∠BDF
∴BF=BD
∵EF//BC
The bdef is a parallelogram
∵BF=EF
The bdef is a diamond