Question

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

• 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 $AB\parallel CD,\angle 1=\angle 2$ [corresponding angles]

as $CD\parallel EF,\angle 2=\angle 3$ [corresponding angles]

Hence, $\angle 1=\angle 3$

Therefore, $AB$ is parallel to $EF.$