Prove theorems about parallel lines and parallelograms using angle relationships.
When a transversal crosses two parallel lines, specific angle pair relationships are formed. These relationships — alternate interior angles, corresponding angles, co-interior (same-side interior) angles — form the foundation of most geometric proofs.
Angle Pair Relationships (parallel lines)
A parallelogram has: opposite sides parallel and equal, opposite angles equal, and diagonals that bisect each other.
An exterior angle of a triangle equals the sum of the two non-adjacent interior angles. If ∠A = 40° and ∠B = 75°, the exterior angle at C equals 40° + 75° = 115°.
Remember This!
In any proof involving parallel lines, explicitly state which lines are parallel and which transversal you are using before citing an angle relationship theorem.
Two parallel lines are cut by a transversal. If one alternate interior angle measures 68°, what does the other measure?