# Ex.6.4 Q2 The-Triangle-and-its-Properties Solutions NCERT Maths Class 7

## Question

Take any point \(\rm{}O\) in the interior of a triangle \(\rm{}PQR\) Is

(i) \(\rm{}OP + OQ > PQ?\)

(ii) \(\rm{}OQ + OR > QR?\)

(iii) \(\rm{}OR + OP > RP? \)

## Text Solution

**What is known? **

Triangle \(PQR\) and point in the interior of triangle.

**What is unknown?**

(i) \(OP + OQ > PQ?\)

(ii) \(OQ + OR > QR?\)

(iii) \(OR + OP > RP?\)

**Reasoning:**

This question is straight forward. If \(\rm{}“o”\) 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 centre \(\rm{}“o”\). 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.

**Steps:**

Yes, \(\rm{}POQ\) forms a triangle

Yes, \(\rm{}OQR\) forms a triangle.

Yes, \(\rm{}ORP\) forms a triangle.