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prove that two distinct lines cannot have more than 1 common point

Posted by Mohammad Asad 4 years, 9 months ago

CBSE > Class 09 > Mathematics

1 answers

Yogita Ingle 4 years, 9 months ago

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 distict point is wrong.
Hence, two lines cannot have more than one point in common.

1Thank You

ANSWER

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CBSE > Class 09 > Mathematics