Consider triangles PBQ, QCR, RDS, and SAP :
AP = PB = CR = RD They are all parallel to each other
BC = CD = DS = SA they are parallel to each other.
angle PBQ = angle QCR = angle RDS = angle SAP = 90 deg.
So all the four triangles are congruent. So PQ = QR = RS = SP
we know that QS and PR are perpendicular to each other, as they are parallel to AB and BC respectively.
hence, PQRS is a Rhombus.