Corresponding angles match in the same position
These two marked angles are in matching corners where the transversal meets each parallel line, so they are equal.
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Same place, same angle size.
Year 8
Angles in parallel lines
Identify corresponding, alternate and co-interior angles, explain why they are linked, and use the facts to find missing angles.
Lesson overview
Geometry — angle facts with parallel lines
When a transversal crosses two parallel lines, the angles are linked in predictable ways. Corresponding angles are equal because they sit in matching positions. Alternate angles are equal because the lines stay the same distance apart and the crossing line makes the same opening. Co-interior angles add to because they make a straight-line pair together inside the parallel lines.
Alternate angles sit inside the lines on opposite sides
These angles are between the parallel lines and on opposite sides of the transversal, so they are equal.
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Inside, opposite sides, equal.
Co-interior angles add to
These two inside angles are on the same side of the transversal, so together they make .
add to
Same side and inside means the pair sums to a straight angle.
Worked example
One of a pair of alternate angles is 64 degrees. Find the other angle.
The two marked angles are alternate, so they are equal.
- Notice that both marked angles lie inside the parallel lines.
- They are on opposite sides of the transversal, so they form a pair of alternate angles.
- Alternate angles are equal.
- So x = 64 degrees.
Try it
Decide first whether the marked angles are corresponding, alternate or co-interior, then use the matching fact.
Question 1
If two corresponding angles are marked on parallel lines, which statement is true?
Question 2
One angle in a pair of alternate angles is 57 degrees. What is the other angle?
Question 3
Two co-interior angles are 112 degrees and x. What is x?
Question 4
Which pair of angles adds to 180 degrees on parallel lines?
Question 5
A corresponding angle is 124 degrees. The angle in the matching position at the second intersection is:
Common mistakes
Watch for these when working through the lesson.
- Using the equal-angle rule for co-interior angles instead of adding to 180 degrees.
- Calling angles alternate even when they are on the same side of the transversal.
- Ignoring angle position and matching by appearance only.
Related topics
These ideas fit closely with this lesson.
- Translations, reflections and rotations.
- Volume of cuboids and prisms.
- Measure and draw angles accurately.