How can you prove that two different lines can’t have more than one point in common?

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To prove = Lines 1 and 2 have only one point in common. Proof = Suppose lines 1&2 intersects at two points say P & Q .Then line 1 contains points P & Q. Also, line 2 contains points P & Q. So two lines 1 & 2 pass through two distinct points P & Q. But only one line can pass through two different points....
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To prove = Lines 1 and 2 have only one point in common. Proof = Suppose lines 1&2 intersects at two points say P & Q .Then line 1 contains points P & Q. Also, line 2 contains points P & Q. So two lines 1 & 2 pass through two distinct points P & Q. But only one line can pass through two different points. Axiom 3. So the assumption we started with that two lines can pass through two distinct point is wrong. Hence, two lines cannot have more then one point in common. read less
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