Answer:
Since, the opposite sides of parallelogram are always congruent.
With using this property, the proof is mentioned below,
Given : Quadrilateral PQRS is a rectangle.
To Prove: PR = QS
Quadrilateral PQRS is a rectangle ( Given )
Rectangle PQRS is a parallelogram. ( Definition of a rectangle )
QP ≅ RS QR ≅ PS ( By the definition of parallelogram)
m∠QPS = m∠RSP = 90° ( Definition of a rectangle )
Δ PQS ≅ ΔSRP (SAS criterion for congruence )
PR ≅ QS ( Corresponding sides of congruent triangles are congruent)
PR = QS ( Congruent line segments have equal measures )
Hence proved.