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Hi,

n,l,m are three lines in the same plane. If l intersects m and n is parallel to m, show that l also intersects n.

Pls guide me in solving this problem. Thanks!

Here is the answer to your question.
Assume l and n do not intersect. Then l || n.
Now, l || n and n ||m (Given)
∴ l || m (Lines which are parallel to a given line are parallel to each other)
This contradicts the given statement that l intersect m. So, our assumption is not correct.
Hence, l and n must intersect.

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Assumelandndo not intersect. Thenl||n.

Now,l||and n||m (Given)Therefore, l||m(Lines which are parallel to a given line are parallel to each other)This contradicts the given statement thatlintersectm. So, our assumption isnotcorrect.Hence,landnmust intersect.
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Lol, why the heck does everything get messed up after posting? o_O I'll post it again so that it will be clear for you to read, bro :P

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Hmm, sorry, I can't change anything about it. The web expert should do something about it...

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Assumelandndo not intersect. Thenl||n.Now,l||n and n||m (Given)∴l||m(Lines which are parallel to a given line are parallel to each other).This contradicts the given statement thatlintersectm. So, our assumption isnotcorrect.Hence,landnmust intersect.
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