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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 : (ii) PQ = SR

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 :

(ii) \small PQ=SR

            

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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 : \small PQ=SR

Proof : In \triangleACD,

      S is mid point of DA.                (Given)

      R  is mid point of DC.               (Given)

  By mid point theorem,

                        \small SR\parallel AC  and   \small SR=\frac{1}{2}AC...................................1

   In \triangleABC,

      P is mid point of AB.                (Given)

      Q  is mid point of BC.               (Given)

  By mid point theorem,

                        \small PQ\parallel AC  and   \small PQ=\frac{1}{2}AC.................................2

From 1 and 2,we get

     \small PQ\parallel SR          and   \small PQ=SR=\frac{1}{2}AC

Thus, \small PQ=SR

 

 

 

 

 

 

   

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