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1 Chpter 7 Answers Alterntive Activities Check students work. 3. The imge hs length tht is 2 3 tht of the originl segment nd is prllel to the originl segment. 4. The segments pss through the endpoints of the dilted segment. 5. The corresponding ngles re congruent. 6. The originl segment nd its dilted imge chnge, ut corresponding ngles remin congruent. Also, the originl segment nd its dilted imge remin prllel. 7. The originl segment nd its dilted imge chnge, ut corresponding ngles remin congruent. Also, the originl segment nd its dilted imge remin prllel. 8. Yes. Explntions should incorporte the findings from Exercises 6 7. Alterntive Activities Check students work. 3. Students cnnot tell tht the lines re prllel y just looking ecuse the lines could intersect off-screen. 4. Answers my vry. Smple: Construct trnsversl nd mesure pir of lternte interior ngles. If those ngles re congruent, the lines re prllel. 5. The construction is impossile, since prllel lines cnnot intersect. 6. Check students work. Some softwre progrms do not recognize the impossiility of the construction. 7. Answers my vry. Smple: Construct pir of prllel lines nd then mnipulte two points on ech segment to crete segment of length 4 cm nd segment of length 6 cm. Then connect the segment endpoints to form trpezoid. Alterntive Activities Check students work. 2. Check students work. Students should select their own scle fctor. 3. Check students work. Students should mintin the sme scle fctor s in Exercise Two 5. Four 6. Answers my vry. Smple: Construct the fourth verticl edge in order to mke ll fces cler. Then hide segment pieces tht re not prt of the cue. Reteching Answers my vry. Smple: Answers my vry. Smple: Reteching l m 1 3 Given If lines, then corr. s re. 2 nd 3 re m3 m2 180 supplementry. Sustitution Def. of supplementry m1 m2 180 Angle Add. Postulte 2 3 Given 3 1 Sustitution If corresponding s, then lines re prllel. 2 1 Verticl s re. Reteching Answers my vry. Smple: Z X Y 2 4. Check students work. 38 Resoning nd Prllel Lines Geometry Chpter 7

2 Reteching Answers my vry. Smple: Reteching Check students work. 5. flse 6. true 7. flse Prctice 7-1: Exmple Exercises 1. corresponding ngles 2. lternte interior ngles 3. sme-side interior ngles 4. lternte interior ngles 5. sme-side interior ngles 6. corresponding ngles in m in. Prctice 7-1: Mixed Exercises 1. 1 nd 5, 2 nd 6, 3 nd 8, 4 nd nd 6, 3 nd nd 5, 3 nd 6 4. Sme-Side Interior Angles Theorem 5. Corresponding Angles Postulte 6. Alternte Interior Angles Theorem in m cm 13. lternte interior ngles 14. corresponding ngles 15. corresponding ngles 16. corresponding ngles 17. lternte interior ngles 18. sme-side interior ngles 4. trpezoid, prllelogrm 5. trpezoid, prllelogrm 6. No; since opposite sides of prllelogrm re prllel, the sme-side interior ngles formed y the djcent sides must e supplementry. Since no two pirs of ngles from the list re supplementry, they cnnot possily form prllelogrm. 7. nd 8. g nd h 9. i nd j, k nd l Prctice 7-2: Mixed Exercises 1. l nd m, converse of Sme-Side Interior Angles Theorem 2. none 3. BC nd AD, Converse of Sme-Side Interior Angles Thm. 4. RT nd HU, Converse of Corresponding Angles Post. 5. BH nd CI, Converse of Corresponding Angles Post. 6. GO nd AI, Tringle Midsegment Thm. 7. Trpezoid; two distinct pirs of sme-side interior ngles re supplementry. 8. Trpezoid; two distinct pirs of sme-side interior ngles re supplementry. 9. Irregulr; no two ngles re supplementry or. 10. Prllelogrm; opp. sides re y the Converse of Sme-Side Interior Angles Thm Prctice 7-3: Exmple Exercises N N Prctice 7-2: Exmple Exercises 1. Becuse diltion is similrity trnsformtion, SCT SC'T '. Corresponding ngles of similr polygons re congruent, so TCS T 'C'S. Since SC' is trnsversl of CT nd C'T', y the Converse of the Corresponding Angles Postulte, CT C'T'. 2. Becuse trnsltion is congruence trnsformtion, ABC DEF. So BCA EFD y CPCTC. BC EF since corresponding ngles re congruent. 3. Resons 1. Given 2. Def. sme-side interior ngles 3. Sme-Side Interior Angles Theorem 4. Given 5. Def. sme-side interior ngles 6. Sme-Side Interior Angles Theorem 7. Two lines to third line re to ech other. Geometry Chpter 7 Resoning nd Prllel Lines N 4. Answers my vry. Smple:

3 5. Answers my vry. Smple: P P P Prctice 7-3: Mixed Exercises 1 3. Q R R T T R 40 Resoning nd Prllel Lines Geometry Chpter 7

4 Answers my vry. Smple: T K 8. c K 14. Answers my vry. Smple: 9. c K Answers my vry. Smple: 11. Answers my vry. Smple: c Prctice 7-4: Exmple Exercises 1. one-point 2. two-point 3. one-point 4. two-point 5. one-point 6. two-point 7. two-point 8. one-point 9. one-point 10. two-point 11. two-point 12. one-point Geometry Chpter 7 Resoning nd Prllel Lines 41

5 Prctice 7-4: Mixed Exercises 1. one-point 2. two-point 3. two-point 4. one-point 5. one-point 6. two-point Answers my vry. Smple: B 16. Answers my vry. Smple: 8. C 17. Answers my vry. Smple: D 9. Prctice 7-5: Mixed Exercises A I B III C II 11. A III B I C II 2. 2 D E Prctice 7-5: Exmple Exercises 1. longitude 2. Yes; lines of longitude re gret circles nd ll gret circles must intersect ecuse no two distinct gret circles cn e prllel. 3. No; the only lines of ltitude tht is gret circle is the equtor. All other lines of ltitude re smller thn gret circle nd re drwn such tht ll point on the sme line of ltitude re equidistnt from the equtor. Hence, no two lines of ltitude cn intersect. 4. No; the only line of ltitude tht is gret circle is the equtor. All other lines of ltitude re smller thn gret circle nd do not intersect ech other. 5. Yes; longitude lines re gret circles ecuse they re the intersection of plne with the center of the sphere nd its two poles. 6. Answers my vry. Smple: 3. 6 F 4. Answers my vry. Smple: 5. Answers my vry. Smple: A 7. E 8. C 9. A 10. H 11. B 12. F 13. G 14. D 42 Resoning nd Prllel Lines Geometry Chpter 7

6 6. Answers my vry. Smple: 12. Answers my vry. Smple: 7. Answers my vry. Smple: A 13. Answers my vry. Smple: Checkpoint: For use fter Alternte Interior Angle Thm. 2. Converse of the Corresp. Angle Post. 3. Corresp. Angle Post. 4. Converse of the Alternte Interior Angle Thm. 5. Sme-Side Interior Angle Thm. 6. Corresp. Angle Post. 7. Converse of the Corresp. Angle Post. 8. Verticl Angle Thm. 9. Converse of the Sme-Side Interior Angle Thm. 10 A 14. two-point 15. one-point 16. Answers my vry. Smple: 11. Answers my vry. Smple: B M p 17. Answers my vry. Smple: A line cn intersect nother line t only one point. This is not true in sphericl geometry ecuse line in sphericl geometry re gret circles, nd two gret circles intersect t two points. 12. E Chpter Assessment, Form A ; Sme-Side Interior Angles Thm.; 55; Alternte Interior Angles Thm ; Corresp. Angle Post. then Angle Addition Post.; 60; Sme-Side Interior Angles Thm ; Alterntive Interior Angles Thm.; 95; Sme-Side Interior Angles Thm ; Corresp. Angle Post.; 105; Angle Addition Post ; Corresp. Angle Post. nd Sme-Side Interior Angle Thm.; 89; Corresp. Angle Post ; Alternte Interior Angle Post.; 115; Sme-Side Interior Angle Post. 7. D Chpter Assessment, Form B ; Corresp. Angle Post.; 120; Alternte Interior Angle Thm ; Sme-Side Interior Angle Thm.; 90; Verticl Angle Thm ; Alternte Interior Angle Thm.; 80; Sme- Side Interior Angle Thm. 4.80; Corresp. Angle Post.; 100; Sme-Side Interior Angle Thm ; Corresp. Angle Post.; 92; Sme-Side Interior Angle Thm ; Corresp. Angle Post. nd Angle Addition Post.; 91; def. of verticl ngles 7. B Answers my vry. Smple: B t Geometry Chpter 7 Resoning nd Prllel Lines 43

7 13. Answers my vry. Smple: TASK 3 Answers my vry. Smple:. t 14. two-point 15. one-point 16. Answers my vry. Smple: Use one-point perspective when the view is stright on, fcing side. Use two-point when the view is t n ngle, fcing corner. 17. Answers my vry. Smple:. TASK 4 Answers my vry. Smple:. Alterntive Assessment TASK 1 Answers my vry. Smple: t. 8 2; 8 4; 8 nd 3 re supplementry c. m2 75, m3 105, m4 75, m5 105, m6 75, m7 105, m8 75 d. 7 nd 4 re supp. Given 4 8 Supp. of the If lt. int s sme re re, then lines re. 7 nd 8 re supp. Angle Add. Post. TASK 2 Answers my vry. Smple:. Cumultive Review 1. C 2. B 3. C 4. C 5. D 6. D 7. C 8. B 9. D 10. A 11. C 12. C 13. A 14. C 15.,, 16. Answers my vry. Smple: A Q P B 17. If the ngles occur in the given order, the qudrilterl is trpezoid. One pir of the trpezoid s sides is prllel y the Converse of the Sme-Side Interior Angles Thm. If the ngles re ordered 60, 120, 60, 120, the qudrilterl is prllelogrm. Both pirs of opposite sides re prllel y the Converse of the Sme-Side Interior Angles Thm. 44 Resoning nd Prllel Lines Geometry Chpter 7

8 Stndrdized Test Prep 1. D 2. D 3. C 4. B 5. D 6. A 7. E 8. C 9. D 10. C 11. C 12. B 13. B 14. Answers my vry. Smple: 15. Answers my vry. Smple: one-point perspective two-point perspective ; Alternte Interior Angle Thm.; 122; Sme-Side Interior Angle Thm. 17. Answers my vry. Smple: Alternte interior ngles, such s 1 nd 4, sme-side interior ngles, such s nd 2, or corresponding ngles, 2 4 such s 1 nd 5, cn e used to prove tht two lines re prllel. 5 6 Geometry Chpter 7 Resoning nd Prllel Lines 45

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