Key Concepts: Proving Lines Parallel

Converses of Parallel Line Theorems

To prove lines are parallel, we use the converses of our earlier theorems:

• Converse of Corresponding Angles Postulate: If corresponding angles are congruent, then the lines are parallel.
• Converse of Alternate Interior Angles Theorem: If alternate interior angles are congruent, then the lines are parallel.
• Converse of Alternate Exterior Angles Theorem: If alternate exterior angles are congruent, then the lines are parallel.
• Converse of Consecutive Interior Angles Theorem: If consecutive interior angles are supplementary, then the lines are parallel.

Other Ways to Prove Lines Parallel

• If two lines are perpendicular to the same Line, they are parallel.
• If two lines have the same slope (in coordinate geometry), they are parallel.