1. Holt McDougal Geometry 3-3 Proving Lines Parallel Warm Up State the converse of each statement. 1. If a = b, then a + c = b + c. 2. If mA + mB = 90°, then A and B are complementary. 3. If AB + BC = AC, then A, B, and C are collinear.

2. Holt McDougal Geometry 3-3 Proving Lines Parallel Use the angles formed by a transversal to prove two lines are parallel. Objective

3. Holt McDougal Geometry 3-3 Proving Lines Parallel Recall that the converse of a theorem is found by exchanging the hypothesis and conclusion. The converse of a theorem is not automatically true. If it is true, it must be stated as a postulate or proved as a separate theorem.

4. Holt McDougal Geometry 3-3 Proving Lines Parallel

5. Holt McDougal Geometry 3-3 Proving Lines Parallel Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. Example 1A: Using the Converse of the Corresponding Angles Postulate 4  8 4  8 4 and 8 are corresponding angles. ℓ || m Conv. of Corr. s Post.

6. Holt McDougal Geometry 3-3 Proving Lines Parallel Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. Example 1B: Using the Converse of the Corresponding Angles Postulate m3 = (4x – 80)°, m7 = (3x – 50)°, x = 30 m3 = 4(30) – 80 = 40 m8 = 3(30) – 50 = 40 ℓ || m 3  8 m3 = m8

7. Holt McDougal Geometry 3-3 Proving Lines Parallel The Converse of the Corresponding Angles Postulate is used to construct parallel lines. The Parallel Postulate guarantees that for any line ℓ, you can always construct a parallel line through a point that is not on ℓ.

8. Holt McDougal Geometry 3-3 Proving Lines Parallel

9. Holt McDougal Geometry 3-3 Proving Lines Parallel m2 = (10x + 8)°, m3 = (25x – 3)°, x = 5 Use the given information and the theorems you have learned to show that r || s. Example 2B: Determining Whether Lines are Parallel m2 = 10x + 8 = 10(5) + 8 = 58Substitute 5 for x. m3 = 25x – 3 = 25(5) – 3 = 122Substitute 5 for x.

10. Holt McDougal Geometry 3-3 Proving Lines Parallel m2 = (10x + 8)°, m3 = (25x – 3)°, x = 5 Use the given information and the theorems you have learned to show that r || s. r || s m2 + m3 = 58° + 122° = 180° m2 = 10x + 8 = 10(5) + 8 = 58 m3 = 25x – 3 = 25(5) – 3 = 122.

11. Holt McDougal Geometry 3-3 Proving Lines Parallel StatementsReasons 1. p || r 5. ℓ ||m 2. 3  2 3. 1  3 4. 1  2 2. Alt. Ext. s Thm. 1. Given 3. Given 4. Trans. Prop. of  5. Conv. of Corr. s Post. Given: p || r, 1  3 Prove: ℓ || m

12. Holt McDougal Geometry 3-3 Proving Lines Parallel Check It Out! Example 3 Given: 1  4, 3 and 4 are supplementary. Prove: ℓ || m

13. Holt McDougal Geometry 3-3 Proving Lines Parallel Check It Out! Example 3 Continued StatementsReasons 1. 1  4 1. Given 2. m1 = m42. Def.  s 3. 3 and 4 are supp. 3. Given 4. m3 + m4 = 1804. Trans. Prop. of  5. m3 + m1 = 180 5. Substitution 6. m2 = m36. Vert.s Thm. 7. m2 + m1 = 180 7. Substitution 8. ℓ || m8. Conv. of Same-Side Interior s Post.

14. Holt McDougal Geometry 3-3 Proving Lines Parallel Classwork/Homework Pg. 166 (1-22 all)