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

(i) OP + OQ > PQ?


(ii) OQ + OR > QR?


(iii) OR + OP > RP?



(i) According to the given condition in the question,


If O is a point in the interior of the given triangle


Then,


Three triangles can be constructed, these are:


and


We know that,


In a triangle, the sum of the length of either two sides of the triangle is always greater than the third side


Therefore,


is a triangle having sides OP, OQ and PQ


As,


OP + OQ > PQ


(ii) According to the given condition in the question,


We have:


If O is a point in the interior of the given triangle


Then,


Three triangles can be constructed, these are:


and


We know that,


In a triangle,


The sum of the length of either two sides of the triangle is always greater than the third side


Therefore,


is a triangle having sides OR, OQ and QR


As,


OQ + OR > QR


(iii) According to the given condition in the question,


We have:


If O is a point in the interior of the given triangle


Then,


Three triangles can be constructed, these are:


and


We know that,


In a triangle,


The sum of the length of either two sides of the triangle is always greater than the third side


Therefore,


is a triangle having sides OR, OP and PR


As,


OR + OP > PR


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