3.2 Properties of Parallel Lines Objectives: TSW … Use the properties of parallel lines cut by a transversal to determine angles measures. Use algebra to find angle measure.

Postulate 3.1 Corresponding Angles Postulate p m n  1   5, If a transversal intersects two parallel lines, then corresponding angles are congruent.  2   6,  3   7,  4   8

Example 1: In the figure, x ‖ y and m  10 = 120 . Find m  14.

Theorem 3.1: Alternate Interior Angles Theorem If a transversal intersects two parallel lines, then alternate interior angles are congruent. p m n  4   5,  3   6

Example 2: In the figure, x ‖ y and m  12 = 38 . Find m  15.

Theorem 3.2: Same-Side Interior Angles Theorem If a transversal intersects two parallel lines, then Same Side Interior Angles are supplementary. p m n m  4 + m  6 = 180,m  3 + m  5 = 180

Example 3: In the figure, x ‖ y and m  12 = 43 . Find m  14.

Theorem 3.3: Alternate Exterior Angles Theorem If a transversal intersects two parallel lines, then alternate exterior angles are congruent. p m n  1   8,  2   7

Example 4: In the figure, x ‖ y and m  11 = 51 . Find m  16.

Example 5: Finding measures of Angles What are the measures of all numbered angles. Which theorem or postulate justifies each answer?

Example 6: What is the measure of  RTV?

Example 7: If m  5 = 2x – 10, m  6 = 4(y – 25), and m  7 = x + 15, find x and y.

Example 8: In the figure, m  3 = 110  and m  12 = 55 . Find the measure of the other angles.

Summary Relationship of angle measures formed by two parallel lines cut by a transversal. Corresponding Angles - congruent Alternate Interior Angles - congruent Alternate Exterior Angles - congruent Same Side Interior Angles - Supplementary