Parallel Lines Proofs
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Terms
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- Angle Addition Postulate
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- Linear Pair Postulate
- If two angles form a linear pair, then they are supplementary; that is, the sum of their measures is 180 degrees.
- Congruent Complements Theorem
- If two angles are complementary to the same angle or to congruent angles, then they are congruent.
- Corresponding Angles Postulate
- If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
- Consecutive Interior Angles Theorem
- If two parallel lines are cut by a transversal, then the pairs of consecutive interior lines are supplementary.
- Alternate Interior Angles Theorem
- If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
- Consecutive Interior Angles Converse
- If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.
- Segment Addition Postulate
- If B is between A and C, then AB + BC = AC.
- Corresponding Angles Converse
- If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel.
- Alternate Exterior Angles Converse
- If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.
- Vertical Angles Theorem
- If two angles are vertical angles, then they are congruent.
- Alternate Interior Angles Converse
- If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.
- Congruent Supplements Theorem
- If two angles are supplementary to the same angle or to congruent angles, then they are congruent.
- Alternate Exterior Angles Theorem
- If two parallel lines are cut by a transversal, then the pairs of exterior angles are congruent.