If two Lines are parallel to a third line then the lines are parallel to each other.

Given: It is given that three lines l, m, and n, and line l ∥ line m and line m ∥ line n.

To Prove:    Line l ∥ Line n

Proof: Let us draw a line p transversal for lines l, m, and n.

For lines l and m with transversal p

∠1 = ∠2 (Corresponding angles)…(1)

 For lines m and n with transversal p

∠2 = ∠3 (Corresponding angles)…(2) 

From (1) and (2)

∠1 = ∠3

But ∠1 = ∠3, are Corresponding angles for lines l and n with transversal p, and Corresponding angles are equal.

Therefore, we can say that line l and n are parallel.
So,  Line l ∥ Line n.

Hence proved.