Same Math › Geometry · grades 9–10 › Parallel lines and transversals
What are the angles made by parallel lines?
When a line (the transversal) crosses two parallel lines, it makes eight angles, and only two sizes. Every angle is either the small size or the big size, and the two sizes add to 180°. Kids learn the names for the pairs: corresponding (same spot), alternate interior (inside, opposite sides), alternate exterior and same-side interior.
- One size: angles 2, 3, 6 and 7 here.
- The other size: angles 1, 4, 5 and 8.
- The two sizes add to 180°.
Why schools teach it
Two sizes explain every pair
Eighth graders explore the angles formed by a transversal (8.G.A.5), and geometry students prove the relationships (HSG.CO.C.9).
Memorizing six names is hard. Noticing there are only two sizes makes it easy: equal-looking angles are equal, and a small and a big angle add to 180°.
At the kitchen table
What to say, and what to skip
Say this
Do these two angles look the same size or different?
Same: equal. Different: they add to 180°.Are they in the same spot at each intersection?
Corresponding.Are they between the parallel lines, on opposite sides?
Alternate interior.Can you set up an equation from that?
Skip this
- Using these rules when the lines aren't parallel.The angle pairs are only equal when the lines are parallel.
- Mixing up interior and exterior.Interior means between the two parallel lines.
- Setting supplementary angles equal.Same-side interior angles add to 180°.
See it in action
If ∠3 = 3x + 10 and ∠6 = 5x − 30 are alternate interior angles
Alternate interior angles are equal
3x + 10 = 5x − 30Solve
40 = 2x, so x = 20Find the angle
3(20) + 10 = 70°
If they were same-side interior angles, the equation would be (3x + 10) + (5x − 30) = 180.
Free practice sheet
Make a parallel lines sheet
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Parents also ask
Which pairs are equal?
Corresponding, alternate interior, alternate exterior and vertical angles.
Which pairs add to 180°?
Same-side interior angles and linear pairs (two angles that form a straight line).
What's a transversal?
Any line that crosses two (or more) other lines.
How do kids remember the names?
Many teachers use letter shapes: F for corresponding, Z for alternate interior, C (or U) for same-side interior.