# 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   $\small SR=\frac{1}{2}AC$

S seema garhwal

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 $\triangle$ACD,

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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