54 9 72 1. 9A 83 1. = 1 2. = 4 2. 3. = 2 3. 4. = 2 5. = 4 4. 5. 3 6. 4 7. 3 8. 6 6. = 6 7. = 1 8. = 4 9. (a) (b) 10. 9. a 5 6 ` = 11 10. 9 11. a F + V - E = 5 + 6-9 = 2 `

55 11. 13. 12.

56 9 5. 6. 14. (a) 1 (b) (c) 15. (a) 2 (b) 1 2 9B 90 7. A D F H 8. GH IH FG IJ 9. 35 1. C 2. B 3. B 4. (a) (b) (c)

57 10. 27 cm 3 cm 3 cm 3 cm 3 cm 32 cm 7 cm 3 cm 7 cm 3 cm 3 cm 32 cm 7 cm 7 cm 13. (a) (i) A C F (ii) A D E (b) A B 14. (a) B F (b) AB GF 32 cm 15. (a) (b) 11. (a) 9C 104 1. 2. (b) 3. 12. (a) (b) 4.

58 9 5. 11. 6. C 7. A 12. 8. 9. 13. 10.

59 14. 16. 17. 15. 18. (a) (b) 6 19. (a) (b) 7

60 9 20. 22. (a) 2 21. (a) 10 (b) (b) (a) (c) (a)

61 9D 119 1. (a) EH = EF ` H EF = EH = 4 cm (b) HG = FG ` H FG = HG = 2 cm (c) HD = DC ` H DC = HD = 6 cm 2. (a) F ABCD C ` F ABCD = FC = 3 cm (b) F ADE E ` F ADE = EF = 8 cm 3. (a) +EBD (b) +BDF 4. (a) A EFGH F (b) A CBGH B (c) A CDEH D 5. (a) FE ABCD MN 6. (a) WS = PQRS WS = QS WQ PQRS QS ` WQ PQRS +WQS (b) WV = PQUV WV = VQ WQ PQUV VQ ` WQ PQUV +WQV 7. (a) EA = ABC EA = AB EB ABC AB ` EB ABC +EBA (b) EF = BCDF EF = BF EB BCDF BF ` EB BCDF +EBF 8. (a) ABCD CDEH CD a AD = CD ED = CD ` ABCD CDEH +ADE a BC = CD CH = CD ` ABCD CDEH +BCH (b) ABCD CDFG CD a AD = CD FD = CD ` ABCD CDFG +ADF a BC = CD CG = CD ` ABCD CDFG +BCG (b) EC ABCD NC

62 9 9. (a) PQGH EFGH GH a FG = GH QG = GH ` PQGH EFGH +QGF a PH = GH EH = GH ` PQGH EFGH +PHE (b) PQGH PQFE PQ a FQ = PQ GQ = PQ ` PQGH PQFE 10. (a) BG = FG (b) +FQG a PE = PQ PH = PQ ` PQGH PQFE +EPH ` B FG = BG = 5 cm 5 cm F C I 6 cm D E G I CI = FE B 3 cm 20 cm ` C EFGH = CI = 4 cm (c) DE = CD DE = FE ` CD FE = DE = 4 cm A 4 cm H 11. (a) BC 2 FE QR (b) AF 2 FU ET (c) (i) A PQRSTU P (ii) A B F C E D Q P U R T S AC AC CDSR ` A CDSR C 12. (a) AC = ABQP AC = AB BC ABQP AB ` BC ABQP +ABC (b) CR = ABC CR = BC BR ABC BC ` BR ABC +RBC (c) PR = ABQP PR = BP BR ABQP BP ` BR ABQP +RBP 13. (a) VM = ABCD VM = AM VA ABCD AM ` VA ABCD +VAM (b) VM = ABCD VM = BM VB ABCD BM ` VB ABCD +VBM

63 (c) VM = ABCD VM = KM VK ABCD KM ` VK ABCD +VKM 14. (a) VPR VQR VR a PR = VR QR = VR ` VPR VQR +PRQ (b) VPQ PQR PQ a 3VPQ 3PQR ` VM = PQ MR = PQ ` VPQ PQR 3. (F) = 6 (V) = 8 (E) = 12 4. (F) = 5 (V) = 5 (E) = 8 5. (a) +VMR 15. (a) VAB VBC VB a AQ = VB CQ = VB ` VAB VBC +AQC (b) VAB VDC V AB a VP VR ` VAB VDC +PVR (c) BE = VAC BE = VE VB VAC VE ` VB VAC +BVE (b) (F) = 7 (V) = 7 (E) = 12 (c) a F + V - E = 7 + 7-12 = 2 ` 6. (a) 9E 126 1. (F) = 7 (V) = 10 (E) = 15 2. (F) = 5 (V) = 6 (E) = 9 (b) (F) = 6 (V) = 8 (E) = 12 (c) a F + V - E = 6 + 8-12 = 2 `

64 9 7. (a) 3. (b) (F) = 7 (V) = 10 (E) = 15 (c) a F + V - E = 7 + 10-15 = 2 ` 127 1. 3 2. 3. 1. 2. 62 3. 1. 1. 2. 3. 4. 3HBC ABCD +HMO 9 129 1. (a) = 2 (b) = 2 2. 2.

65 3. (a) 5. (a) (b) (b) 4. (a) 1 2 4 5 B (b) 1 3 4 5 (c) GH AH

66 9 6. (a) (c) (i) (ii) BF = CDEF BF = CF BC CDEF CF ` BC CDEF +BCF AE = CDEF AE = CE AC CDEF CE ` AC CDEF +ACE (b) 8. (a) (b) 7. (a) (i) C ABFE F (ii) AD ABFE AE (iii) BD ABFE BE = 2 9. (a) (i) 2 (b) ABCD ABFE AB a EA = AB AD = AB ` ABCD ABFE +DAE a BC = AB BF = AB ` ABCD ABFE +CBF (ii) (b) (i) (ii) 1 2 1

67 10. (a) 13. (a) (b) (b) 11. (a) (b) (i) (ii) H C J GH BC 14. (a) 12. (a) (b) (c) IL AB (b) 11

68 9 15. (a) PCFQ ABGH PQ a BP = PQ PC = PQ ` PCFQ ABGH 18. (a) +BPC a GQ = PQ QF = PQ ` PCFQ ABGH +GQF (b) AD = CDEF AD = DF AF CDEF DF ` AF CDEF +AFD (c) BP = BCFG BP = BF PF BCFG BF ` PF BCFG +PFB 16. (a) AE CDSR MD (b) BQ ETSD ET (c) AM = CDSR AM = MS AS CDSR MS ` AS CDSR +ASM 17. (a) PM = ABCD PM = DM PD ABCD DM ` PD ABCD +PDM (b) PM = ABCD PM = KM PK ABCD KM ` PK ABCD +PKM (c) BC = 3PAB BC = PB PC 3PAB PB ` PC 3PAB +CPB (b) (F) = 7 (V) = 7 (E) = 12 19. (a) ABCD (b) (i) ` +DCB = 90c a ECB ` +DCE = 180c - +DCB (ii) = 180c - 90c = 90c BF BG ` BG = BF = 8 cm 3BAG 2 2 AG = BG + AB 2 2 = 8 + 192. cm = 20. 8 cm 3BCF 2 2 CF = BF + BC = 8 2 + 6 2 cm = 10 cm CE CF ` CE = CF = 10 cm

69 (iii) CD = AB = 19.2 cm 3CED DE = CD 2 2 + CE 2 2 = 19. 2 + 10 cm = 21. 6 cm 0.1 cm (c) AH AG ` AH = AG = 20. 8 cm DH DE ` DH = DE = 21. 6 cm 20. (a) 3BCE (b) A BE = CE 2 2 + BC 2 2 = 6 + 8 cm = 10 cm ` E AB = BE = 10 cm F D 20 cm B G E 8 cm 6 cm G C ABEF 3BCE = 1 2 ` # BE # CG 1 2 # BE # CG = 1 2 # 6 # 8 cm2 5CG = 24 cm CG = 4.8 cm C 134 1. B, D A A N M L C B A D I II C A G B, D I, L B III J, M F H I C AB AD BC DE 2 I II A 1 2 II B ( D) ` I 1 a 7 ` I = (7-1) = 6 2 6 II A B II 3 a 7 ` II = (7-3) = 4 E K J ` C ABEF = CG = 48. cm

70 9 III 3 AL 2 6 B 6 3 AL 2 AL 2. M L G B A F M L G B A F 3. (a) C LM IJ B B3 I J ` F H I E K J F H I E K J

71 (c) (i) (ii) AF 4 BD PR QS CE PR 2 QS 2 BD 4 (d) CE 4 A P C B M Q S D E R (b) (a) 9 11 (i) (ii) F M BCDE AM = CM ` CA BCDE CM 4. (a) [ A B X X ] (iii) AM = BCDE AM = PM AP BCDE PM ` AP BCDE +APM (iv) ACD FCD CD a AQ = CD FQ = CD ` ACD FCD +AQF X (b) ABFD APFR AQFS

72 9 136 140 1. C 2. C 3. B 4. B ` 9 5. D EB = BC ` EC ABCD BC 6. C VAB VBC VB a AB = VB BC = VB ` 3VAB 3VBC +ABC 7. A GP = EFGH GP = GE EP EFGH GE ` PE EFGH +GEP 8. B 9. D