Which statement describes a parallelogram that must be a square? (a) A parallelogram with diagonals that bisect each other and opposite sides that are congruent. A parallelogram with perpendicular diagonals. A parallelogram with diagonals that are congruent and perpendicular. A parallelogram with diagonals that are congruent and opposite sides that are congruent.

Consider a parallelogram with diagonals that are congruent and perpendicular.In triangles Δ AOB and Δ AOD,OA = OA (common)OB = OD (Since the diagonals of a parallelogram bisect each other)∠ AOB = ∠ AOD = 90° (diagonals are perpendicular)Therefore, Δ AOB ≅ Δ AOD (By SAS postulate)Since, corresponding parts of congruent triangles are equal,AB = ADSimilarly, we can proveBC = CD and CD = DASo, AB = BC = CD = DA.Also, it is given that AC = BD.Hence, ABCD is a square.Therefore, the correct statement is:A parallelogram with diagonals that are congruent and perpendicular.