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

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Proof

Let us consider that the two lines intersect in two distinct point 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. Given two distinct points, there is a uniqueline that passes through them.Hence our assumption is wrong that the two line can pass through two distinct points is wrong.Hence two distinct lines cannot have more than one point in common. • 39

Theorem 5.1 two distinct lines cannot have more than one point in common.

Proof:-Here we are given two lines l and m. We need to prove that they have only onepoint in common.For the time being, let us suppose that the two lines intersect in two distinct points,say P and Q. So, you have two lines passing through two distinct points P and Q. Butthis assumption clashes with the axiom that only one line can pass through two distinctpoints. So, the assumption that we started with, that two lines can pass through twodistinct points is wrong.From this, what can we conclude? We are forced to conclude that two distinctlines cannot have more than one point in common.

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