What you’ll learn
Prove angle relationships with parallel lines.
Key idea
Vertical-angle reasoning stays at one intersection; corresponding-angle reasoning connects parallel-line intersections.
Vertical angles are local; cross-intersection equalities need parallelism and correct corresponding/alternate positions.
Worked example
Complete missing statements or reasons in a proof for 'Prove angle relationships with parallel lines'.
Lines l and m are given parallel and crossed by t. X and Y occupy matching upper-right positions at distinct intersections; mX=85 degrees. Complete the missing statement and proof reason.
- Given l parallel m permits the corresponding-angle theorem.
- Matching positions at distinct intersections are corresponding, not vertical; transfer X measure to Y.
Answer: mY=mX=85 degrees — corresponding angles of parallel lines cut by a transversal are congruent.
Quick Check
Complete missing statements or reasons in a proof for 'Prove angle relationships with parallel lines'.
Lines l and m are given parallel and crossed by t. X and Y occupy matching upper-right positions at distinct intersections; mX=50 degrees. Complete the missing statement and proof reason.