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Warm Up State the converse of each statement. 1. If a = b , then a + c = b + c .

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. Objective.

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Warm Up State the converse of each statement. 1. If a = b , then a + c = b + c .

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  1. 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. Objective Use the angles formed by a transversal to prove two lines are parallel.

  3. 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. Example 1A: Using the Converse of the Corresponding Angles Postulate Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. 4 8 4 8 4 and 8 are corresponding angles. ℓ || mConv. of Corr. s Post.

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

  6. 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.

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

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

  9. Given:p || r , 1 3 Prove: ℓ || m 1.p || r 1. Given 2.3  2 2. Alt. Ext. s Thm. 3. Given 3.1  3 4.1  2 4. Trans. Prop. of  5. Conv. of Corr. s Post. 5. ℓ ||m

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

  11. Check It Out! Example 3 Continued 1. Given 1.1  4 2. m1 = m4 2.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3 6. Vert.s Thm. 7. m2 + m1 = 180 7. Substitution 8. ℓ || m 8. Conv. of Same-Side Interior sPost.

  12. Classwork/Homework • Pg. 166 (1-22 all)

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