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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 : (i) SR || AC and SR = 1/2 AC

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 :

                 (i)  \small SR\parallel AC  and   \small SR=\frac{1}{2}AC

                 

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

Proof: In \triangleACD,

      S is the midpoint of DA.                (Given)

      R  is the midpoint of DC.               (Given)

  By midpoint theorem,

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

   

 

 

 

 

 

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