Question

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

• A. AB and EF are perpendicular to each other.
• B. AB and EF intersect each other, but not at right angles.
• C. AB and EF are parallel to each other.
• D. We cannot say anything about AB and EF.

Answer 1

The correct option is C AB and EF are parallel to each other.

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, $\angle 1=\angle 2$ (corresponding angles)

as CD || EF, $\angle 2=\angle 3$ (corresponding angles)
Hence,
$\angle 1=\angle 3$

Therefore, AB is parallel to EF.