1. Ch. 3.3 I can prove lines are parallel Success Criteria:  Identify parallel lines  Determine whether lines are parallel  Write proof Today’s Agenda Check HW # 18 Do Now Lesson Assignment Do Now: 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. If a + c = b + c, then a = b. If  A and  B are complementary, then m  A + m  B =90°.

2. Ch. 3.3 I can prove lines are parallel Success Criteria:  Identify parallel lines  Determine whether lines are parallel  Write proof Today’s Agenda Check HW # 22 ONLINE Do Now Lesson Assignment Do Now: State the converse of each statement. 1. If AB + BC = AC, then A, B, and C are collinear If A, B, and C are collinear, then AB + BC = AC.

3. A 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.

6. Use the given information and the theorems you have learned to show that r || s. Example 2A: Determining Whether Lines are Parallel  4   8  4   8  4 and  8 are alternate exterior angles. r || sConv. Of Alt. Ext.  s Thm.

7. 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. r || s Conv. of Same-Side Int.  s Thm. m  2 + m  3 = 58° + 122° = 180° 2 and 3 are same-side interior angles.

8. 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. Example 3: Proving Lines Parallel Given: p || r,  1   3 Prove: ℓ || m

9. Assignment #23 pg 160-163 #8 – 10, 13 -28 Green Assignment Sheets Success Criteria: Can You???  Identify parallel lines  Determine whether lines are parallel  Write proof

10. Check It Out! Example 2b Refer to the diagram. Use the given information and the theorems you have learned to show that r || s. m  3 = 2x , m  7 = (x + 50) , x = 50 m  3 = 100  and m  7 = 100   3   7r||s Conv. of the Alt. Int.  s Thm. m  3 = 2x = 2(50) = 100°Substitute 50 for x. m  7 = x + 50 = 50 + 50 = 100° Substitute 5 for x.

11. Check It Out! Example 3 Given:  1   4,  3 and  4 are supplementary. Prove: ℓ || m

12. Check It Out! Example 3 Continued (can skip this slide) 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 || m 8. Conv. of Same-Side Interior  s Post.