Question

Two lines which are both parallel to the same line, are parallel to each other. Prove the theorem.

Answer 1

Given: Three lines l,m,n in a plane such that m ll l and n || l.

To prove: m || 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. This is a contradiction. So, our supposition is wrong. Hence m || n.