由L1‖L2,MQ⊥L1,NP⊥L1,∴MQ⊥L2,NP⊥L2,∴四边形PQMN是矩形,由∠MAB=∠NDA,∠MBA=∠NAD,AB=AD,∴△ABM≌DAN（A,S,A）∴AM=DN,AN=BM,同理可证AM=BQ=CP,BM=OQ=DP,∴MN=NP=PQ=QM,∴四边形PQMN是正方形.证毕....