Prove by contradiction that two distinct lines in a plane cannot intersect in more than one point.

Suppose two distinct lines l and m intersect at a point P.

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

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

We know that,

Given two distinct points, there exists one and only one line passing through them.

So our assumption is wrong.

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