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