∵正方形abcd
∴ab=bc,∠abc=∠bcd=90
∵be=cf
∴△abe全等于△bcf
∴ae=bf,∠eab=∠fbc,∠bea=∠cfb
∵∠eab+∠bea=90,∠fbc+∠cfb=90
∴∠fbc+∠bea=90
∴ae⊥bf