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AQA GCSE Mathematics · 8300
AQA 8300 · G3 Angle Properties Check the specification (PDF) (opens in a new tab)
Imagine two parallel lines crossed by a third straight line, called a transversal. This makes two intersections and eight angles. The parallel lines are often marked with matching arrows in a diagram. Their angles are related because each parallel line meets the transversal at the same inclination.
The matching positions give corresponding angles, such as . Opposite sides of the transversal give interior alternate angles and exterior alternate angles .
Look for angles in the same relative position at the two intersections: for example, one below and to the right at the upper intersection and one below and to the right at the lower intersection. These are corresponding angles. When the two lines are parallel, corresponding angles are equal. In the diagram, .
You can picture moving the angle at the upper intersection down the transversal without turning it. Because the lines are parallel, it fits the angle in the matching position at the lower intersection.
Alternate angles lie at different intersections on opposite sides of the transversal. They must also be either both inside the parallel lines or both outside them. Both types are equal when the lines are parallel. In the diagram, is an interior alternate pair, while is an exterior alternate pair.
Suppose in the diagram. The corresponding angle is , and the interior alternate angle is also . If you need angle , it sits next to on a straight line, so . A problem may need more than one angle fact: identify each pair or straight line as you use it.
When a transversal crosses parallel lines:
Check the parallel-line markings, then state the angle fact used. For the labelled diagram, (corresponding), (interior alternate) and (exterior alternate). Adjacent angles on a straight line sum to .
Check that the lines are parallel before using alternate or corresponding angle facts.
Give the reason for each angle you find, such as ‘corresponding angles on parallel lines are equal’. Use these terms rather than informal letter-shape names.
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Parallel lines
Two straight lines in the same plane that remain the same distance apart and never meet.
Transversal
A line that crosses two or more other lines at different points.
Corresponding angles
Angles at different intersections that occupy the same position relative to a transversal and the two lines it crosses. They are equal when those lines are parallel.
Alternate angles
Angles at different intersections on opposite sides of a transversal, either both between the two lines or both outside them. They are equal when those lines are parallel.
Put your knowledge into practice — try past paper questions for Mathematics
Parallel lines
Two straight lines in the same plane that remain the same distance apart and never meet.
Transversal
A line that crosses two or more other lines at different points.
Corresponding angles
Angles at different intersections that occupy the same position relative to a transversal and the two lines it crosses. They are equal when those lines are parallel.
Alternate angles
Angles at different intersections on opposite sides of a transversal, either both between the two lines or both outside them. They are equal when those lines are parallel.