3.3 Parallel Lines and Transversals

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Presentation transcript:

3.3 Parallel Lines and Transversals CAS 4, 7 3.3 Parallel Lines and Transversals Goal 1: Properties of Parallel Lines Goal 2: Properties of Special Pairs of Angles

Postulate 15 Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 2

Theorems About Parallel Lines Thm 3.4 Alternate Interior Angles Thm If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 3 4

Theorems About Parallel Lines (continued) Thm 3.5 Consecutive Interior Angles Thm If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary 5 6 Are supplementary

Theorems About Parallel Lines (continued) Thm 3.6 Alternate Exterior Angles Thm If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. 7 8

Theorems About Parallel Lines (continued) j Thm 3.7 Perpendicular Transversal Thm If a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other. h k

Ex. 1 Use properties of parallel lines to find the value of x.

Ex. 2 Line n and m are parallel. Solve for x.

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