Question

Prove that two distinct lines cannot have more than one point in common.

Answer 1

Given: Two distinct line l and m

To Prove: Lines l and m have at most one point in common.

Proof: Two distinct lines l and m intersect at a point P.

Let us suppose they will interact at another point, say Q (different from P).

It means two lines l and m passing through two distinct point P and Q.

But it is contrary to the axiom 5.1 which states that “Given two distinct points, there exists one and only one line pass through them”

So our supposition is wrong

Hence, two distinct lines cannot have more than one point in common