Question

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

Answer 1

Proof:
Let us consider that two lines intersect at two distinct points P and Q.
Thus, we see that the two lines l and m pass through two distinct points P and Q.
But this assumption clashes with the axiom, which states that “given two distinct points, there is a unique line that passes through them.”
Thus, our assumption that two lines can pass through two distinct points is wrong.
So, two distinct lines cannot have more than one point in common.



Hence proved.