Warm-Up Classify the angle pair as corresponding, alternate interior, alternate exterior, consecutive interior or vertical:

Section 3 – 3 Prove Lines are Parallel

Postulate 16 Corresponding Angles Converse: If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.

Theorem 3.4 Alternate Interior Angles Converse: If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel. 4 5

Theorem 3.5 Alternate Exterior Angles Converse: If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel. 1 8

Theorem 3.6 Consecutive Interior Angles Converse: If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel. 3 5

Theorem 3.7 Transitive Property of Parallel Lines: If two lines are parallel to the same line, then they are parallel to each other. If p || q and q || r, then p || r. q p r

Example 1 Find the value of y that makes a || b. Explain. (5y + 6)° 121° 5y + 6 = y = 115 b a 5 5 y = 23 Alternate Exterior Angles Converse

Example 2 Find the value of x that makes m || n. Explain. 2x° 54° 2x + 54 = x = 126 n m 2 2 x = 63 Consecutive Interior Angles Converse

Homework Section 3-3 Page 165 – – 8, 10 – 15, 19 – 23, 31, 34

Example 2 Prove that g || h. Given: 4 = 5 Prove: g || h. Statement Reasons 1. 4 = 5 1 g 5 h 4 Given 3. 1 = 5 Vertical Angles ˜ ˜ ˜ 2. 1 = 4 ˜ Transitive Property 4. g || h Corresponding Angles Converse