Axiom 5.1

Chapter 5 Class 9 Introduction to Euclid's Geometry
Concept wise

## Two distinct lines cannot have more than one point in common.

Given : Two distinct lines l 1   and l 2

To Prove : l 1   and l 2 cannot have more than 1 point in common

Proof : We will prove this by contradiction.

Let  l 1   & l 2  have two points in common, P & Q.

Now, by Axiom 5.1
Given two distinct points, there is a unique line that passes through them.

Thus, only one line passes through two distinct points P & Q.

But here we assumed both l 1   & l 2   pass through P & Q.

So, our assumption is wrong.

Therefore,

Two distinct lines cannot have more than one point in common.

Hence proved

Thus, only one line passes through two distinct points P & Q.

But here we assumed both l 1   & l 2   pass through P & Q.

So, our assumption is wrong.

Therefore,

Two distinct lines cannot have more than one point in common.

Hence proved

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