Prove that 2 distinct lines cannot have more than one point in common
Prasad , 8 Years ago
Grade 9
Algebra> Prove that 2 distinct lines cannot have m...
1 Answers
Arun
To prove = Lines l1 and l2 have only one point in common.
Proof =
suppose lines l1 and l2 intersect at two disticnt points say P and Q.Then l1 contains points P and Q.
Also, l2 contains points P and Q.
So two line sl1 and l2 pass through two distinct points P and 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 disticnt point is wrong.
Hence, two lines cannot have more than one point in common.
Proof =
suppose lines l1 and l2 intersect at two disticnt points say P and Q.Then l1 contains points P and Q.
Also, l2 contains points P and Q.
So two line sl1 and l2 pass through two distinct points P and 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 disticnt point is wrong.
Hence, two lines cannot have more than one point in common.
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