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Two parallel lines + one transversal = equal angles
Alternate interior angles and corresponding angles: the patterns to spot to solve 90% of angle problems.
The fact to remember
When two parallel lines are cut by the same transversal, two pairs of angles are automatically equal:
- Corresponding angles (« inverted Z » pattern).
- Alternate interior angles (« Z » pattern).
The pattern to spot
The mental shortcut
Draw a mental « Z » between the two parallel lines: the two angles at the « tips » of the Z are alternate interior → equal.
Related cases (all equal to α)
- Corresponding: angles at the same position around each intersection (« F » pattern).
- Vertically opposite: the two angles opposite at an intersection are equal.
The reverse trick: proof of parallelism
If you observe that two alternate interior angles are equal, then the lines are necessarily parallel. This is one of the most-used criteria in geometric proofs.
?Your turn
Two parallel lines are cut by a transversal. One angle measures 65°. What's its alternate interior?
#angles#parallel#transversal#alternate-interior