Question

If P,Q and R are three points on a line, and Q lies between P and R, then prove that PQ + QR = PR

Answer 1

Step-by-step explanation:

Given :-

P,Q and R are three points on a line, and Q lies between P and R.

To find:-

If P,Q and R are three points on a line, and Q lies between P and R, then prove that PQ + QR = PR

Solution:-

P,Q and R are the three points on a line

Q lies between P and R

=>Q is the mid point of P and R

=>PQ = PR - QR

By Euclid's fourth axiom :

" Things that which coincide with each other are equal to each other"

=>PQ +QR = PR

And since Q is the mid point then

The distance between PQ = The distance between QR

PQ = QR

=>PQ+PQ = PR

=>2 PQ = PR

or =>2QR = PR

Answer:-

If P,Q and R are three points on a line, and Q lies between P and R, PQ + QR = PR and PR = 2PQ = 2 QR

Used formula:-

Euclid's Axiom :-

• " Things that which coincide with each other are equal to each other"

Additional information:-

• Euclid wrote 13 books in geomerty these collection of 13 books is called "The Elements".
• He was the first mathematician who wrote geometry in a such a way , so he is regarded as the father of geometry .