Question 146552
To prove that PQRS is a Rhombus, we need to prove PQ = QR = RS = SP.

In fact, triangles ASP, BPQ, CQR and DSR are congruent because
< A = < B = < C = < D
AP = PB = CR = RD
AS = SD = BQ = QC

Thus
PQ = QR = RS = SP