S is any point in the interior of a `trianglePQR` . Prove that `SQ +SR lt PQ +PR`

In the figure X is any point in the interior of triangle. Point X is joined to vertices of triangle. Seg PQ|| set DE, set QR|| set EF. Fill in the blanks to prove that set PR|| seg DF.

Take any point O in the interior of a triangle PQR. Is OP+OQ>PQ? ? (ii) OQ+OR>QR? (iii) OR+OP>RP?

If Q is a point on the side SR of a triangle PSR such that PQ=PR then prove that PS > PQ

If S is a point on side PQ of a triangle PQR such that PS = QS = RS, then PR^(2) + QR^(2) = ……………..

In the given figure, Q is a point on the side SR of DeltaPSR such that PQ = PR. Prove that PS gt PQ.

Let O be any point in the interior of DeltaABC , prove that : AB+BC+CA lt 2 (OA+OB+OC)

In the figure given below PS is the bisector of angleQPR of DeltaPQR . Prove that (QS)/(SR) =(PQ)/(PR) .

In the given figure, PS=PR, angleTPS=angleQPR . Prove that PT=PQ .

If S is the mid-point of side QR of a DeltaPQR , then prove that PQ+PR=2PS .