Question

Two lines, AB and EF, are parallel to a third line, CD. What relationship exists between the two lines?

• A. The two lines will be perpendicular to each other
• B. The two lines intersect each other but not at right angles
• C. They are parallel to each other
• D. Their relationship cannot be determined

Answer 1

The correct option is C

They 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.