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Geometry › Parallel lines
Parallel lines
Two lines that never meet — and the angle pairs that appear when a third line cuts across them.
Parallel lines & a transversal
Tilt the transversal. Same-position angles always match.
slope ≈ 60°
60°
Corresponding
60° = 60° (same position)
Alternate
Alternate interior angles match
Co-interior
60° + 120° = 180°
The setup
Two parallel lines and a transversal — a third line that crosses both. At each crossing, four angles form. Compare them across the two crossings and you get three named pairs.
The three pair rules
- Corresponding angles — same position at each crossing — are equal.
- Alternate angles — on opposite sides of the transversal, between or outside the parallels — are equal.
- Co-interior (allied) angles — same side, between the parallels — sum to 180°.
Why it works
Both parallels make the same angle with the transversal — that's what "parallel" means. So whatever the angle is at one crossing, the same angle has to appear at the other.
Other pairs at one crossing
- Vertically opposite angles (across the X) are equal.
- Adjacent angles on a straight line sum to 180°.
Using the rules
When you know one angle, all eight angles in the diagram fall out. This is how problems involving train tracks, ladders against walls, or zig-zag patterns get solved — find one angle and chase the others.