# prove two distinct lines cannot hace more than one point in common?

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let us suppose that two distinct  lines have 2 points in common,but a line consists of 2 points. this means the two lines are coincident, this means whatever we supposed was wrong and two distinct  lines cannot have two points in common. further a line consists of two points so two distinct lines cannot have more than 2 points in common and earlier we have proved two distinct lines cannot have 2 points in common. this means two distinct lines cannot have more than one point in common.

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let us suppose that two distinct  lines have 2 points in common,but a line consists of 2 points. this means the two lines are coincident, this means whatever we supposed was wrong and two distinct  lines cannot have two points in common. further a line consists of two points so two distinct lines cannot have more than 2 points in common and earlier we have proved two distinct lines cannot have 2 points in common. this means two distinct lines cannot have more than one point in common

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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 one point 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. But this assumption clashes with the axiom that only one line can pass through two distinct points. So, the assumption that we started with, that two lines can pass through two distinct points is wrong. From this, what can we conclude? We are forced to conclude that two distinct lines cannot have more than one point in common.

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