Shown below are two lines, AB and EF, which are parallel to a common line CD. Let K be the transversal passing through the three lines.
We know that if a transversal intersects two parallel lines then the corresponding angles are equal.
as AB || CD, ∠1 = ∠2 (corresponding angles)
as CD || EF, ∠2 = ∠3 (corresponding angles)
Hence, ∠1 = ∠3
Therefore, AB is parallel to EF.