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Quiz tomorrow on 3-1 and 3-2

Quiz tomorrow on 3-1 and 3-2. Use can use your textbook’s online tutorials to study: http://www.classzone.com/cz/books/geometry_2007_na/book_home.htm?state=CT - this resource is multi-faceted and is created by the authors of the class textbook. Help With the Math

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Quiz tomorrow on 3-1 and 3-2

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  1. Quiz tomorrow on 3-1 and 3-2 • Use can use your textbook’s online tutorials to study: • http://www.classzone.com/cz/books/geometry_2007_na/book_home.htm?state=CT - this resource is multi-faceted and is created by the authors of the class textbook. • Help With the Math • @HomeTutor has lessons with audio! • PowerPoint Presentations are a great way to go back and review a lesson. • Practice, Practice, Practice • eWorkbook has extra practice problems for each chapter. • Assessment • Section Quizzes allows you to take practice quizzes that are immediately scored for you with feedback!

  2. 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. L4 ≅L8 L4 ≅L8 L4 and L8 are corresponding angles. ℓ || mConv. of Corr. Angles Post.

  3. 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. mL3 = (4x – 80)°, mL7 = (3x – 50)°, x = 30 mL3 = 4(30) – 80 = 40Substitute 30 for x. mL8 = 3(30) – 50 = 40 Substitute 30 for x. mL3 = mL8 Trans. Prop. of Equality L3 ≅L8 Def. of ≅ angles. ℓ || m Conv. of Corr. Ls Post.

  4. You Try! Exercise 1 Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. mL1 = mL3 L1 ≅L3 L1 and L3 are corresponding angles. ℓ || mConv. of Corr. Angles Post.

  5. You Try! Exercise 2 Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. mL7 = (4x + 25)°, mL5 = (5x + 12)°, x = 13 mL7 = 4(13) + 25 = 77Substitute 13 for x. mL5 = 5(13) + 12 = 77 Substitute 13 for x. mL7 = mL5 Trans. Prop. of Equality L7 ≅L5 Def. of ≅ Angles. ℓ || m Conv. of Corr. Ls Post.

  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 2A: Determining Whether Lines are Parallel Use the given information and the theorems you have learned to show that r || s. L4 ≅L8 L4 ≅L8 L4 and L8 are alternate exterior angles. r || sConv. Of Alt. Int. Angles Thm.

  8. You Try! Exercise 3 Refer to the diagram. Use the given information and the theorems you have learned to show that r || s. mL4 = mL8 L4 ≅L8 Def of Congruent angles L4 ≅L8 L4 and L8 are alternate exterior angles. r || sConv. of Alt. Int. Angles Thm.

  9. Example 3: Proving Lines Parallel Given:p || r , L1 ≅L3 Prove:ℓ || m

  10. Example 3 Continued 1. Given 1.p || r 2.L3 ≅L2 2. Alt. Ext. Angles Thm. 3.L1 ≅L3 3. Given 4.L1 ≅L2 4. Trans. Prop. of ≅ 5.ℓ ||m 5. Conv. of Corr. Ls Post.

  11. Check It Out! Example 3 Given: L1 ≅L4, L3 and L4 are supplementary. Prove:ℓ || m

  12. Check It Out! Example 3 Continued 1. Given 1.L1 ≅L4 2. mL1 = mL4 2.Def. Congruent Angles 3.L3 andL4 are supp. 3.Given 4. mL3 + mL4 = 180° 4. Def. of Supplementary 5. mL3 + mL1 = 180° 5. Substitution (Step 2  4) 6. mL2 = mL3 6. Vert. Angles Thm. 7. mL2 + mL1 = 180° 7. Substitution (Step 6  5) 8.ℓ || m 8. Conv. of Same-Side Interior AnglesPost.

  13. Check It Out! Example 4 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. Angles Post.

  14. Lesson Quiz: Part I Name the postulate or theorem that proves p || r. 1. L4 ≅L5 Conv. of Alt. Int. LsThm. 2. L2 ≅L7 Conv. of Alt. Ext. LsThm. 3. L3 ≅L7 Conv. of Corr. LsPost. 4. L3 and L5 are supplementary. Conv. of Same-Side Int. Angles Thm.

  15. Lesson Quiz: Part II Use the theorems and given information to prove p || r. 5. mL2 = (5x + 20)°, m L7 = (7x + 8)°, and x = 6 mL2 = 5(6) + 20 = 50° mL7 = 7(6) + 8 = 50° mL2 = mL7, so L2 ≅L7 p || r by the Conv. of Alt. Ext. AnglesThm.

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