S is a point on side QR of a triangle PQR. Show that: PQ + QR + RP 2PS

Given : A triangle PQR. A point S on QR.

To Prove : PQ + QR + PR 2PS

Proof : We know that sum of two sides of a triangle is greater than the third side.

PQ + QS PS --(1)

PR + SR PS --(2)

Adding (1) and (2) on both sides, we get,

PQ + QS + PR + SR PS + PS= PQ + QS + SR + PR 2PS= PQ + QR + PR 2PS

Hence proved.