Question

5. IF PORS is a quadrilateral, then show that: PO+OR + RS + PS > 2 (PR + OS)​

Answer 1

We know that in any triangle the sum of any two sides is greater than the third side.

In △PQO,PQ+QO>PQ→(1)

In △SOP,SO+PO>PS→(2)

In △SOR,SO+OR>RS→(3)

In △QOR,QO+OR>QR→(4)

Adding equations (1) , (2) , (3) & (4) , we get

2(PO+OQ+SO+OR)>PQ+QR+RS+SP

PQ+QR+RS+SP<2(PQ+OR+SO+OQ)

PQ+QR+RS+SP<2(PR+SQ)