3-5 Using Properties of Parallel Lines Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

Warm Up Answer the questions. 1. What are parallel Lines? 2. When two parallel lines are intersected by a transversal, then corresponding angles are supplementary? 3. Linear Pair Angles are complementary. Coplanar lines that do not intersect and have same slope No, corresponding angles are congruent. No Linear pair angles are supplementary 3.5 Using Properties of Parallel Lines

Use the properties of parallel lines in real-world situations. Objective 3.5 Using Properties of Parallel Lines

Recall that when two parallel lines are cut by a transversal special angle relationships are created. Corresponding, alternate exterior, alternate interior angles are congruent. Consecutive interior angles are supplementary. 3.5 Using Properties of Parallel Lines

Check It Out! Example 1 What if…? Suppose the corresponding angles on the opposite side of the boat measure (4y – 2)° and (3y + 6)°, where y = 8. Show that the oars are parallel. 4y – 2 = 4(8) – 2 = 30° 3y + 6 = 3(8) + 6 = 30° The angles are congruent, so the oars are || by the Conv. of the Corr. s Post. 3.5 Using Properties of Parallel Lines

Lines m, n and k represent three of the oars on the picture. m|| n and n || k. Prove that m || k. Example 2: Proving Two Lines are Parallel 3.5 Using Properties of Parallel Lines

Example 2 Continued StatementsReasons 1. m || n 5. 1  3 2. 1  2 3. n || k 4. 2  3 2. Corresponding Angles 1. Given 3. Given 4. Corresponding Angles 5. Transitive Property 3.5 Using Properties of Parallel Lines 6. m || k6. Converse of corresp. <s

Check It Out! Example 3 Given: 1  4, 3 and 4 are supplementary. Prove: ℓ || m 3.5 Using Properties of Parallel Lines

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. 3.5 Using Properties of Parallel Lines

Lesson Quiz: Part I Name the postulate or theorem that proves p || r. 1. 4   5Conv. of Alt. Int.  s Thm. 2.  2   7 Conv. of Alt. Ext. s Thm. 3.  3   7Conv. of Corr.  s Post. 4.  3 and  5 are supplementary. Conv. of Same-Side Int.  s Thm. 3.5 Using Properties of Parallel Lines

Lesson Quiz: Part II Use the theorems and given information to prove p || r. 5. m2 = (5x + 20)°, m  7 = (7x + 8)°, and x = 6 m2 = 5(6) + 20 = 50° m7 = 7(6) + 8 = 50° m2 = m7, so 2 ≅ 7 p || r by the Conv. of Alt. Ext. s Thm. 3.5 Using Properties of Parallel Lines