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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.
 

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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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