Conditions for Parallel Lines
Theorem. Converse of Alternate Interior Angles Theorem
If two lines are cut by a transversal so that a pair of alternate interior angles is congruent, then the lines are parallel.
| Given: |
and are alternate interior angles.
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| Prove: |
Proof:
Theorem. Converse of Alternate Exterior Angles Theorem
If two lines are cut by a transversal so that a pair of alternate exterior angles is congruent, then the lines are parallel.
Prove the theorem as an exercise.
