Chapter 2. Chapter 2 5. Section segments: AB, BC, BD, BE. 32. N 53 E GEOMETRY INVESTIGATION Answers will vary. 34. (a) N. sunset.

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1 Chpter 2 5 Chpter N 53 E GEOMETRY INVESTIGATION Answers will vry. 34. () N Setion segments: AB, BC, BD, BE sunset sunrise 4. 2 rys: CD (or CE ), CB (or CA ) 6. ED, EC, EB W Oslo, Norwy E 8. () (d) () PQR or RQP, PQS or SQP, SQR or RQS PQS nd SQR, PSQ nd RSQ S N 12. () 6 ngles 2 2 pirs: WSV nd VST, WSU nd UST W sunset Cui, Brzil sunrise E 14. () 85 ute 129 otuse 100 otuse 16. AOB = 78, BOC = , S N 20. X = points, 6 lines; 5 points, 10 lines; n( n 1) 6 points, 15 lines; n points, lines 2 W sunset sunrise Ushui, Tierr del Fuego E 24. () (d) S 26. () (d) () (d) () S 17 E or N 17 W S 61 W or N 61 E S E or N W (d) N W or S E 38. ABC = A: N 60 W, S 60 E B: S 20 W, N 20 E C: S 36 E, N 36 W D: N 38 E, S 38 W

2 6 Chpter ngle: 5π 14 π 2π, ngle: Seleted Extended Prolems : O, T, W 90 : J, P, U, X 135 : K, Q, V, Y 180 : D, L, R 225 : C, E, I, M, S 270 : B, F, N 315 : A, G, H, Z Setion () GHI, MNO ABC, DEF, JKL PQR, JKL, MNO (d) ABC, PQR (e) None, sed on the given informtion 4. () One of mny orret exmples 120 ngle: One of mny orret exmples One of mny orret exmples () (d) Impossile; ll ngles must e less thn 90 for the tringle to e ute. 6. () Five tringles: , , 6-9-9, 8-8-8, Seven tringles: , , , , , , One tringle: () (d) 8 (e) Mny urves re possile.

3 Chpter () 24. () (d) 14. () No - not ll line segments Yes No - rosses itself (d) Yes (e) No - retres itself 16. () 26. () 18. () BDFH BCDG, ABDG, or BDEG ABG, BDG, GDE, BCD, or ACE (d) ABG, BDG, GDE, BCD, or ACE (e) EFI (f) BHG, ABH, GDF, or DEF (g) ABDG, BDEG, or BCDG (h) ABDE, BCEG, or ACDG (i) DIE (g) BDEH, or BDFA (k) BCDGH, BCDFG, BCDFH, ABDIE, BDIEH, or BDJEH 20. () (d) () () Yes, 2 Yes, () Yes, 1 No 32. () Pentgon: Four - 72, 144, 216, 288 Hexgon: Five - 60, 120, 180, 240, 300 Otgon: Seven - 45, 90, 135, 180, 225, 270, 315 n 1

4 8 Chpter Prts (),,, (d), (f), nd (h) hve oth types of symmetry. Prts (e) nd (g) hve refletion symmetry only. 36. () Isoseles right tringles nd squres re used. There is no refletion symmetry. There is one rottion symmetry of 180 out the enter of the lok. Squres re used. There re four xes of refletion symmetry: horizontl line through the enter, vertil line through the enter, nd oth digonls. There re three rottion symmetry out the enter of the lok: 90, 180, nd 270. Retngles nd squre re used. There re two xes of refletion symmetry: horizontl line through the enter nd vertil line through the enter. There is one 180 rottion symmetry out the enter of the lok. (d) Right isoseles tringles, squres, rhomuses, nd n otgon re used. There re four xes of refletion symmetry: horizontl line through the enter, vertil line through the enter, nd oth digonls. There re three rottion symmetries out the enter of the lok: 90, 180, nd 270. Setion () 6. () WXY = 107, XYZ = 54, YZW = 113, ZWX = 86. The ngle sum should e 360. Answers my vry slightly due to mesurement error. TUP = 114, UPQ = 126, PQR = 125, QRS = 139, RST = 98, STU = 118 ; The ngle sum should e 720. Answers my vry slightly due to mesurement error. 8. () Yes. The sum of the ngle mesures is 180. No. The sum of the ngle mesures is 200. No. The sum of the ngle mesures is = 45, = 45, = 65, d = 80, e = 30, f = 70, g = 20, h = () , (d) 110, 76, 117, sides () (d) (e) (f) () (d) Equilterl tringle, squre, regulr hexgon, regulr otgon, regulr 12-gon, regulr 24- gon

5 Chpter () Mny nswers re possile. One solution is shown. 4. () (ii) Mny nswers re possile. One solution is shown The mesure of one vertex ngle in regulr otgon is 135, whih is not ftor of Polygon V D T Tringle Qudrilterl Pentgon Hexgon Otgon n-gon n( n 3) n n CBA = () Not losed. The ngle mesure sum is Closed. The ngle mesure sum is Quilt lok designs will vry. Surrounding ny vertex, the sum of the mesures of the ngles is 360. Completed squre quilt loks will form regulr tesselltion. Four 90 ngles ompletely surround vertex with no gps. Seleted Extended Prolems 35. () The mesures of A, B, nd C dd up to 180 sine they form stright ngle. Tht is, + + = 180. Retngle, 1 2 AC. Yes, the results re the sme. Setion () Not polyhedron. It hs hole. Not polyhedron. A polyhedron is not urved. Polyhedron 8. () MPTQ, NOSR MNOP, OSTP, MNRQ, RSTQ MNRQ, NOSR, RSTQ (d) Right trpezoidl prism 10. () Right isoseles trpezoidl prism Olique pentgonl prism () Right regulr pentgonl pyrmid Olique squre pyrmid

6 10 Chpter nd 18. There is one xis of symmetry with order All of the nswers for prolem 6 re possile nets. 22. (ii) Bse F V F + V E Tringle Qudrilterl Otgon n-gon n+1 n+1 2n+2 2n Yes, Euler's formul holds for these figures. Bse F V F + V E Tringle Qudrilterl Pentgon n-gon 2n+2 2n 4n+2 4n Yes, Euler's formul holds for these figures. 38. () Equilterl tringle Retngle Hexgon (d) Pentgon 40. () Right pentgonl prism Right irulr one Sphere (d) Regulr dodehedron Setion m 2. () 1 m 1000 g 1 kg 1 m 10 mm 1 L (d) 1000 ml fes; One possile polyhedron is n olique pentgonl pyrmid. 4. () 60 min 1 deg 1 dy 24 hours (d) 1000 mm 1 m 1 ft 12 in. 30. () Sphere Right irulr ylinder 32. () Cirle Isoseles tringle xes: one s shown through the middle of the top nd ottom fes, one through the middle of the front nd k fes, nd one through the middle of the left nd right fes. 36. () There re four xes of symmetry eh of order 3. One suh xis is shown l 1 slug, 1 kg 2.2 l, 1 hyl 9.8 kg, 1 glug 0.1 hyl 8. () g km 96,000 oz (d) dys 10. () 42, m in in. (d) m 12. () 10 mi/qt 3.64 mi/hr 500 g/m (d) ents/ml 14. () 1.57 ents/m ft/min mi/hr ft/hr 20. $ $39.97

7 Chpter ourses tons/month 28. () (d) 0.35 rdin (e) 5.24 rdins (f) 2.71 rdins Seleted Extended Prolems 30. A it is the fundmentl memory unit in ll omputer systems. 1 kiloit = 1024 its = 2 10 its 1 megit = 1024 kiloits = 2 10 kiloits 1 yte = 8 its 1 kiloyte = 1024 ytes = 2 10 ytes 1 megyte = 1,048,576 ytes = 2 20 ytes 1 gigyte = 1,073,741,824 ytes = 2 30 ytes