Prove that the two lines which are both parallel to the same line, are parallel to each other.
Given Three lines l, m and n in a plane such that
l ll n and m ll n.
To prove l ll m
Proof If possible, let l is not parallel to m. Then, l and m should intersect at a unique point, say P.
Thus, through a point P, outside n, there are two lines l and m, both parallel to n.
This contradicts the parallel lines axiom.
So, our assumption was wrong.
Hence, l ll m