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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