Question

If P, Q, R are three non collinear points, then what is PQ ∩ PR equal to ?​

Answer 1

Step-by-step explanation:

Given: PR is a single line segment.

P,Q & R are the three points on a line.

If Q becomes the mid point of line segment PR; then we have: PQ=QR.

So, by means of construction we will get:

(1) Take a mid point of 1st part of line segment PQ as A. So we get: PA=AQ & PA+AQ=PQ.

(2) Similarly, for line segment QR as 2nd part of line segment taking the mid point as B we have:

QB=BR.

Comparing both the cases we have:

PQ=PA+AQ and QR=QB+BR.

Therefore a line segments having mid point of mid points we get: Q a mid point of AB and A and B are the mid points of PQ & QR respectively.

Thus, PQ+QR=PR. Hence proved.