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### Proving Lines Parallel

• Postulates:
• If two lines in a plane are cut by a transversal so that corresponding angles are congruent, then the lines are parallel
• If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel
• Parallel Postulate: IF there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line
• Theorems:
• If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel
• If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the lines are parallel
• In a plane, if two lines are perpendicular to the same line, then they are parallel

## Proving Lines Parallel

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