Angles with parallel lines
Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles
What a learner can do afterwards
- Identify alternate, corresponding, and co-interior angle pairs in a diagram with parallel lines
- Explain why alternate angles are equal using the concept of translation along the transversal
- Find missing angles in a parallel-line diagram using a combination of angle relationships
The lesson
When two parallel lines are crossed by another line, called a transversal, eight angles are formed. Some of these angles are always equal to each other, and some always add up to 180 degrees. Once you know which pairs do what, you can find any missing angle without measuring a thing.
Corresponding angles sit in the same spot at each crossing point, like the top-left corner at both intersections. Trace a line through them and you get an F-shape. Corresponding angles are always equal.
Alternate interior angles sit between the two parallel lines, on opposite sides of the transversal. They trace a Z-shape (or S-shape). Slide (translate) along the transversal and one parallel line lands exactly on the other, carrying each angle onto its alternate partner. That is why alternate angles are always equal.
A diagonal path crosses two parallel roads. Where it meets the first road, the angle above the road is 65 degrees. The alternate interior angle at the second road, on the opposite side of the path, is also 65 degrees. The co-interior angle right next to it, on the same side of the path, is 180 - 65 = 115 degrees, because co-interior angles always add up to 180.
Spot the shape first. An F finds corresponding angles, a Z finds alternate angles, and a C (or U) finds co-interior angles. Once you know the shape, you know the rule.
Corresponding angles match (F-shape), alternate angles match (Z-shape), and co-interior angles add up to 180 degrees (C-shape).
Watch it
Where it sits
Learn first
This opens up
Nothing builds on it yet.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.