Alternate angles equal, corresponding angles equal, co-interior angles sum to 180°.
Key formulas
Three packs
Name the transversal. Then decide which pack you need. Mixing alternate with corresponding is a classic error.
Prove parallel
Conversely, if a pair of alternate angles are equal, the lines are parallel — useful in written proofs.
Numbers
Corresponding angle 72° → matching corresponding is 72°. Co-interior partner is 108°.
Worked example
Worked example
Problem. Two parallel lines are cut by a transversal. One angle is 110°. Find its alternate interior angle and its co-interior angle.
Solution. Alternate interior = 110°. Co-interior sums to 180°, so co-interior = 70°.
Z, F, C
Z-shape for alternate, F for corresponding, C for co-interior.
Review quiz
One angle between parallels is 65°. Its alternate interior angle is:
Practice questions
- Two parallels cut by a transversal. One angle is 110°. Find its alternate and its co-interior.
- State the converse used to prove two lines parallel.
Study notes
Do the lines have to be horizontal?
No — parallelism is about direction, not orientation on the page.
More in Plane Geometry
- Circle tangents: the radius is perpendicular
- Right-triangle lengths: Pythagoras and altitude
- Similar triangles: matching sides in proportion
- Chord theorem: perpendicular from the centre
- Isosceles triangles and equal base angles
- Alternate segment theorem with a short proof
- Converse of Pythagoras: proving a right angle
- Heron’s formula when height is hidden