Question

Take any point O in the interior of a triangle PQR . is OP+QQ >PQ

Answer 1

  yes. As, OPQ forms another triangle in PQR,..
as per the rule for formation of triangles,
length of a side of a triangle < sum of the other two sides,

In triangle OPQ,

OQ<PQ+OP
OP<PQ+OQ
hence, PQ<OP+OQ

Answer 2

If O is a point in the interior of a given triangle, then three triangles ΔOPQ, ΔOQR, and ΔORP can be constructed. In a triangle, the sum of the lengths of either two sides is always greater than the third side.

(i) Yes, as ΔOPQ is a triangle with sides OP, OQ, and PQ.

OP + OQ > PQ

(ii) Yes, as ΔOQR is a triangle with sides OR, OQ, and QR.

OQ + OR > QR

(iii) Yes, as ΔORP is a triangle with sides OR, OP, and PR.

OR + OP > PR