$證明：∵點(diǎn)?F、??E、??M、??N?分別是?AO、??BO、??CO、??DO?的中點(diǎn)$
$∴?EF ?是?△AOB?的中位線，?FN?是?△AOD?的中位線，$
$?MN?是?△COD?的中位線，?EM?是?△BOC?的中位線$
$∴?EF//AB，??FN//AD，?$
$?\frac {EF}{AB}=\frac {FN}{AD}=\frac {MN}{CD}=\frac {EM}{BC}=\frac {1}{2}?$
$∵?EF//AB，??FN//AD?$
$∴?∠EFO=∠BAO，??∠NFO=∠DAO?$
$∴?∠EFN=∠BAD?$
$同理可得：?∠FNM=∠ADC，??∠NME=∠DCB，??∠MEF=∠CBA?$
$∵?\frac {EF}{AB}=\frac {FN}{AD}=\frac {MN}{CD}=\frac {EM}{BC}?$
$∴平行四邊形?ABCD∽?平行四邊形?FEMN?$
