Given : PQRS is a rectangle.

To Prove : PR = QS

Proof:As each rectangle is a parallelogram and PQRS is a rectangle

Therefore PQRS is a parallelogram 

PS = QR  '................(1) [ Opposite sides of a parallelogram]

As each angle of a rectangle is a right angle

In

   PS = QR         [ From Equation 1 ]

        [ Each right angle ]

  RS = RS          [ Common ]

   [By SAS Congruence Criteria]

PR = QS   [ CPCT]

Hence Proved

Given : PQRS is a parallelogram such that  PR  = QS.

To Prove : PQRS is a rectangle

Proof: In

   PR = QS         [ Given ]

  PS = QR          [ Opposite sides of parallelogram ]

  RS = RS          [ Common ]

   [By SSS Congruence Criteria]

    --------(1)   [ CPCT]

As PQRS is a parallelogram, PS || QR

Now PS || QR and RS is the transversal

          [ Co interior angles are supplementary ]

     [ Replacing R from equation 1]

Now PQRS is a parallelogram in which one angle is a right angle.

Therefore PQRS is a rectangle

Hence Proved

Solution: PQRS is a rectangle and we know that diagonals of a rectangle are equal

Each rectangle is aparallelogram and we know that diagonals of a parallelogram bisect each other

Therefore  OS = OR    [ Because when diagonals are equal halves are equal ]

In , As OS = OR

         [Angles opposite equal side are equal ]

Now is the exterior angle of

      [ because  ]

Now each angle of a rectangle is a right angle.