16.2 Angles in parallel lines — Learn

Prerequisites: use straight-line and vertically opposite angle facts. Parallel lines never meet, however far they extend.

Objectives: identify corresponding, alternate and co-interior angles and use their facts to calculate unknown angles. This covers G3.

A transversal crosses parallel lines

A transversal is a line that crosses two other lines. When those lines are parallel, matching angles have useful relationships:

• corresponding angles are equal;
• alternate angles are equal;
• co-interior angles on the same side of the transversal add to $180^\circ$.

Example 1. A corresponding angle is $71^\circ$. Find its matching angle.

Corresponding angles are equal for parallel lines, so the angle is $71^\circ$.

Example 2. An alternate angle is $113^\circ$. Find the unknown alternate angle.

Alternate angles are equal for parallel lines, so the unknown angle is $113^\circ$.

Example 3. Co-interior angles are $x^\circ$ and $68^\circ$. Find $x$.

Co-interior angles on the same side of a transversal sum to $180^\circ$.

Watch out. Equal-looking positions do not prove lines are parallel. Use the parallel-line fact only when the diagram states the lines are parallel or you have proved it.

Progress check

A straight path crosses two parallel tile borders. One acute angle is $68^\circ$. What is the co-interior angle on its side? Give the angle fact.

You should now be able to

• recognise corresponding, alternate and co-interior angle pairs;
• use equality for corresponding and alternate angles;
• use a sum of $180^\circ$ for co-interior angles.