If L, M and N are three straight lines, such that L || M and L || N, prove that M || N.

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Solution

Given:L, M and N are three straight lines, such that L || M and L || N.
To Prove :M || N

Proof: Suppose M is not parallel to N. Then, M and N intersect at a point, say P. Now, P is not on L.
Since, P is on M and M || L
Through a point P, outside L , there are two lines M and N both parallel to L
This is absurd.
Therefore, our supposition is wrong.
Hence, M || N.

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