Prove theorems about lines and angles: vertical angles, parallel-line angle relationships, and perpendicular bisectors.
Select a parallel-line converse from angle evidence
Problem
Decide whether the lines are proved parallel from this complete configuration: a transversal cuts distinct coplanar lines \(\ell~\) and \(m\); \(\text{one}~\text{corresponding}-\angle~\text{pair}\) is congruent.
This argument starts with an angle relationship and seeks a line relationship, so the theorem direction must run from congruence to parallelism. We’ll classify the marked pair by its repeated corner position, verify the transversal and coplanar lines, and then apply the matching converse.
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