Question

Prove that, two lines which are both parallel to the same line, are parallel to each other.

Answer 1

Given: Three lines l,m,n in a plane such that m $\parallel$ l and n $\parallel$ l.

To prove: m $\parallel$ n
Proof: If possible, let m be not parallel to n. Then, m and n intersect in a unique point, say P.
Thus, through a point P outside l, there are two lines m and n both parallel to l, which is a contradiction

So, our supposition is wrong. Hence m $\parallel$ n.