$證明:(1)∵四邊形ABCD是平行四邊形$
$∴AD//CB,∴∠OED=∠OFB$
$∵點(diǎn)O是口ABCD對(duì)角線的交點(diǎn)$
$∴OD=OB$
$在△ODE和△OBF中\(zhòng) $
$\begin{cases}{ ∠OED=∠OFB }\ \\ { ∠DOE=∠BOF } \\{ OD=OB} \end{cases}$
$∴△ODE≌△OBF(AAS)$
$(2)由(1)知，△ODE≌△OBF,∴DE=BF$
$∵點(diǎn)O是BD的中點(diǎn)且 EF⊥BD$
$∴直線EF為BD的垂直平分線，∴DE=BE=BF=DF=15cm$
$∴四邊形BEDF的周長(zhǎng)為4×15=60(cm)$
