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

Solution:

If 'O' is a point in the interior of a given triangle, then the three triangles can be constructed.

You must join all the three vertices of a triangle with the center 'O'.

This question is based on a property that in a triangle the sum of lengths of any two sides is always greater than the third side.

i) Yes, POQ forms a triangle and we know that in a triangle the sum of lengths of any two sides is always greater than the third side.

Thus, OP + OQ > PQ

ii) Yes, OQR forms a triangle and we know that in a triangle the sum of lengths of any two sides is always greater than the third side.

Thus, OQ + OR > QR

iii) Yes, ORP forms a triangle and we know that in a triangle the sum of lengths of any two sides is always greater than the third side.

Thus, OR + OP > RP

☛ Check: NCERT Solutions for Class 7 Maths Chapter 6

Video Solution:

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

NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.4 Question 2

Summary:

We have taken a point O in the interior of a triangle PQR. (i)Yes, POQ forms a triangle, thus, OP + OQ > PQ (ii)Yes, OQR forms a triangle, thus, OQ + OR > QR (iii)Yes, ORP forms a triangle, thus, OR + OP > RP

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