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# ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig 8.29). AC is a diagonal. Show that : (iii) PQRS is a parallelogram.

Q : 1      ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig $\small 8.29$). AC is a diagonal. Show that :

(iii) PQRS is a parallelogram.

Views

Given :   ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig $\small 8.29$). AC is a diagonal.

To prove : PQRS is a parallelogram.

Proof : In PQRS,

Since,

$\small PQ\parallel SR$      and       $\small PQ=SR$.

So,PQRS is a parallelogram.

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