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Take any point O in the interior of a triangle PQR. Is: R (i) OP + OQ > PQ ?

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Take any point O in the interior of a triangle PQR. Is: 

(i) OP + OQ > PQ ?

(ii) OQ + OR > QR ?

(iii) OR + OP > RP ?

Since sum of two sides is greater than third side.

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Join OR, OQ and OP. 

(i) Is OP + OQ > PQ ? 

Yes, POQ form a triangle. 

(ii) Is OQ + OR > QR ?

 Yes, RQO form a triangle. 

(iii) Is OR + OP > RP ?

  Yes, ROP form a triangle.

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