<Qua-2025-797>, hint

suppose a parallelogram ABCD and P,Q,R,S be the midpoint of  side AB,BC,CD,DA

respectively. Since PS=QR=1/2 BD  and  for AQ=AR =a ,triangles ABQ and ADR be congruent, 

Thus BQ=DR, say BC=AD 

Hence ABCD  should be a rhombus.