∴∠D=∠B=90，AB=AD=BC=CD，

In Rt△ABE and Rt△ADF,

∫AB = ADAE = AF，

∴Rt△ABE≌Rt△ADF(HL)，

∴BE=DF.

(2) The quadrilateral AEGF is a diamond.

Proof: ∫△ABE?△ADF,

∴∠BAE=∠DAF，

∵ quadrilateral ABCD is a square,

∴AC split ∠ Not good,

∴∠EAC=∠FAC，

AE = AF，

∴AO vertically divides EF,

∴OE=OF，

OG = OA，

∴ Quadrilateral AEGF is a parallelogram,

AE = AF，

A parallelogram is a diamond.

Pure hand tour, hope to accept.