Question

chapter : Triangle and Its Properties
so solve the questions by its properties
Pls solve it step by step as answers I know but want the steps to write in book ​

Answer 1

Answer:

(i) OP + OQ > PQ;

(ii)  OQ + OR > QR

(III) OR + OP > RP

Step-by-step explanation:

O is a point in the interior of ΔPQR.

Since, O is in the interior of ΔPQR, OPQ will form a triangle.  So will POR and POQ.

We know that, shortest path between any two points in a given plain is the Straight line between those two points.  If O was lying on PQ, we could say, OP + OQ = PQ

Now since O is in the interior of ΔPQR

∴ PQ < OP + OQ i.e. (i) OP + OQ > PQ.

This gives a property of any triangle:

Sum of any two sides is greater than the third side.

Applying the above property in ΔOQR and ΔOPR:

(ii) OQ + OR > QR

And, (III) OP + OR > PR.