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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.