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Name ________________________________________ Date __________________ Class__________________ LESSON 3-3 Reading Strategies Use a Graphic Organizer Line a and line b are parallel. This can be proven in four different ways. In Exercises 1–4, use the given information to determine the theorem or postulate that proves m || n. 1. ∠1 ≅ ∠7 _________________________________________________________________________________________ 2. m∠4 + m∠5 = 180° _________________________________________________________________________________________ 3. ∠5 ≅ ∠3 _________________________________________________________________________________________ 4. ∠8 ≅ ∠4 _________________________________________________________________________________________ 5. If m∠1 = 47° and m∠5 = 49°, are the lines parallel? Explain. _________________________________________________________________________________________ 6. If m∠3 = 119°, what does the measure of ∠6 need to be to prove m || n? _________________________________________________________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 3-26 Holt McDougal Geometry 5. Problem Solving 1. m∠1 = (8x − 1) = 8(4) − 1 = 31° Replace x with 4. Statements m∠2 = (6x + 7) = 6(4) + 7 = 31° Replace x with 4. 1. a. m ⊥ n ∠1 and ∠2 are corr. ∠s and they are congruent, so the shelf is parallel to the rafter by the Conv. of Corr. ∠s Post. Reasons 1. Given 2. b. m∠1 = 90°, m∠2 = 90° 2. Def. of ⊥ 2. m∠3 = (3y + 7) = 3(21) + 7 = 70° Replace y with 21. m∠4 = (5y + 5) = 5(21) + 5 = 110° Replace y with 21. m∠3 + m∠4 = 70° + 110° = 180° ∠3 and ∠4 are supp. ∠s , so the sign posts are parallel by the Conv. of Same-Side Int. ∠s Thm. 3. A 4. J 5. m∠1 = 40° and m∠2 = 40°, so the sides are || by the Conv. of the Alt. Int. ∠s Thm. 6. m∠3 = 90° and m∠4 = 90°, so the sides are || by the Conv. of the Same-Side Int. ∠s Thm. 3. ∠1 ≅ ∠2 3. c. Def. of ≅ ∠s 4. m∠1 + m∠2 = 180° 4. Add. Prop. of = 5. d. ∠1 and ∠2 are a linear 5. Def. of linear pair pair. 6. All the borders are straight lines, and the Colorado–Utah border is a transversal to the Colorado–Wyoming and the Colorado–New Mexico borders. Because the transversal is perpendicular to both borders, the borders must be parallel. Practice C 1. Reading Strategies 1. Converse of the Alternate Exterior Angles Theorem 2. Converse of the Same-Side Interior Angles Theorem 3. Converse of the Alternate Interior Angles Theorem 4. Converse of the Corresponding Angles Postulate 5. No; ∠1 ≅/ ∠5. 6. 61° 2. Because BD must be shorter than BE , x < 11. Therefore BC is the shortest segment. If x = 1, then BD would be the second shortest segment, but if x = 3, then AB would be the second shortest segment. So there is not enough information given in the figure to say which is the second shortest segment. 3-4 PERPENDICULAR LINES Practice A 1. perpendicular; midpoint 2. perpendicular 3. AB ; x < 23 4. FE ; x > 8 5. parallel 6. congruent 7. perpendicular 8. 6 9. 5 3. The distances are equal. 10. 7 Practice B 1. PR ; x < 3.5 2. HJ ; x > 7 4. x = 3, y = 3. AB ; x > 9 3 , z = −1 2 4. UT ; x < 17 Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. A25 Holt McDougal Geometry