Q

# 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) $\small PQ=SR$

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 : $\small PQ=SR$

Proof : In $\triangle$ACD,

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 $\triangle$ABC,

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, $\small PQ=SR$

Exams
Articles
Questions