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(A) Let the mid-points of sides $PQ, QR, RS,$ and $SP$ be $A, B, C,$ and $D$ respectively.According to the Mid-point Theorem,in $	riangle PQS,$ $AD \

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diagonals of $PQRS$ are perpendicular.

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(A) Let the mid-points of sides $PQ, QR, RS,$ and $SP$ be $A, B, C,$ and $D$ respectively.According to the Mid-point Theorem,in $	riangle PQS,$ $AD \parallel QS$ and $AD = \frac{1}{2} QS.$Similarly,in $	riangle RQS,$ $BC \parallel QS$ and $BC = \frac{1}{2} QS.$Thus,$AD \parallel BC$ and $AD = BC,$ which makes $ABCD$ a parallelogram.For $ABCD$ to be a rectangle,its adjacent sides must be perpendicular (i.e.,$AB \perp AD$).Since $AB \parallel PR$ and $AD \parallel QS,$ the condition $AB \perp AD$ implies $PR \perp QS.$Therefore,the quadrilateral formed by joining the mid-points is a rectangle if the diagonals of the original quadrilateral $PQRS$ are perpendicular.

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral $PQRS,$ taken in order,is a rectangle,if

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