∴∠DAQ+∠DQA=90，∠CDP+∠CPD=90，∠DQA+∠CDP=90

∴∠DAQ=∠CDP

∫AD = DC，∠ADQ=∠DCP=90

∴△ADQ≌△DCP

∴DQ=CP

ABCD is a square

∴OD=OC,∠ODQ=∠OCP=45

∴△DOQ≌△COP

∴∠DOQ=∠COP

∴∠DOQ+∠QOC=∠QOC+∠COP=90

∴OQ⊥OP