If two lines, AB and EF, are parallel to a third line, CD, then what can we say about the lines AB and EF?
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.