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Answers to Odd Numbered Problems

( \newcommand{\kernel}{\mathrm{null}\,}\)

Section 1.1

1. 6

3. x=9, AC=24.

5. 15

7. 3

Section 1.2

1. CBD or DBC

3. AED or DEA

5. ABC or CBA

7. 70

9. x=130, y=50

11. x=30, y=60

13. A=60, B=50, C=70

15. A=110, B=80, C=70, D=100

17.

Screen Shot 2021-01-21 at 10.57.58 AM.png

19.

Screen Shot 2021-01-21 at 10.58.22 AM.png

21.

Screen Shot 2021-01-21 at 10.58.55 AM.png

23.

Screen Shot 2021-01-21 at 10.59.03 AM.png

25. 35

27. 30

Section 1.3

1. (a) 53 (b) 45 (c) 37 (d) 30

3. 15

5. 30

7. (a) 150 (b) 143 (c) 90 (d) 60

9. 30

11. x=3,3

13. 10

15. x=70,y=110,z=70

17. x=30,y=45,z=105

19. x=y=z=90

21. x=40,y=80,z=100

23. 8, -8

25. 4, -5

27. 45

Section 1.4

1. x=50,y=z=130

3. u=x=z=120,t=v=w=y=60

5. 55

7. 50

9. 50

11. 55

13. 60

15. 37

17. 11

19. alternate interior: ABD & CDBAB||CD; ADB & CBDAD||BC

21. corresponding: BAC & EDCAB||DE; ABC & DECAB||DE

23. interior on same side of transversal: BAD & CDAAB||CD; ABC & DCBAB||CD

25. alternate interior: BAC & DCAAB||DE; ABC & ECBAB||DE

27. 65

Section 1.5

1. 85

3. 37

5. 60

7. 30

9. 6

11. 120

13. x=50,y=40,z=50

15. 65

17. 8

19. 24

21. 720

23. 60

25. 108

Section 1.6

1. 2/3

3. 6

5. x=1,AB=2

7. x=9,ACB=90

9. 25x+116,372

11. 5

Section 2.1

1. AB=DE,BC=EF,AC=DF,A=D, B=E,C=F,x=5,y=6

3. AB=CD,BC=DA,AC=CA,BAC=DCA,B=D,BCA=DAC,x=55,y=35

5. PQRSTU

7. ABCABD

9. ABDCDB

Section 2.2

1. BC=1.7, =30, C=90

3. BC=1.95,B=99,C=41

5. B

7. D

9. (1) AC,A,AB of ABC=DF,D,DE of DEF

(2) ABCDEF

(3) x=65,y=45

11. (1) AB,B,BC of ABC=EF,F,FD of EFD

(2) ABCEFD

(3) x=40,y=50

13. (1) AB,B,BC of ABC=ED,D,DF of EDF

(2) ABCEDF

(3) x=8

15. (1) AB,B,BC of ABC=ED,D,DF of EDF

(2) ABCEDF

(3) x=20,y=30

17. (1) BA,A,AC of ABC=DC,C,CA of CDA

(2) ABCCDA

(3) x=22

19. (1) AC,ACD,CD of ACD=BC,BCD,CD of BCD

(2) ACDBCD

(3) x=50

21. (1) AD,ADC,DC of ACD=BD,BDC,DC of BCD

(2) ACDBCD

(3) x=2

23. (1) BC,BCA,CA of ABC=DC,DCE,CE of EDC

(2) ABCEDC

(3) x=20,y=10

25. (1) AC,ACB,CB of ABC=EC,ECD,CD of EDC

(2) ABCEDC

(3) x=70

Section 2.3

1. BC=1.9,AC=2.3,C=90

3. BC=2.3,AC=1.9,C=90

5. AB

7. DF

9. (1) ABCDEF

(2) ASA=ASA: A,AB,B of ABC=D,DE,E of DEF

(3) x=5,y=6

11. (1) RSTUWV

(2) AAS=AAS:T,R,RS of RST=V,U,UW of UWV

(3) x=7,y=6

13. (1) ABDCDB

(2) ASA=ASA:B,BD,D of ABD=D,DB,B of CDB

(3) x=30,y=25

15. (1) ABCEDC

(2) ASA=ASA:A,AC,ACB of ABC=E,EC,ECD of EDC

(3) x=11,y=9

17. (1) ACDBCD

(2) AAS=AAS:A,ACD,CD of ACD=B,BCD,CD of BCD

(3) x=5,y=5

19. (1) ABCEDC

(2) ASA=ASA:B,BC,BCA of ABC=D,DC,DCE of EDC

(3) x=2,y=3

21. (1) ABCEDF

(2) ASA=ASA:B,BC,C of ABC=D,DF,F of EDF

(3) x=2,y=3

23. PTBSTB, ASA=ASA:PTB,TB,TBP of PTB=STB,TB,TBS of STB. SB=PB=5,SP=SB+BP=5+5=10.

25. DECBAC, ASA=ASA:E,EC,ECD of DEC=A,AC,ACB of BAC.AB=ED=7.

Section 2.4

1. A=D given, AB=DE given, B=E given, ABCEDF. (ASA = ASA, AC = DF\) corresponding sides of 's are =.

3. AC=EC given, ACB=ECD vertical 's, BC=DC given, ABCEDC. SAS=SAS,AB=ED corresponding sides of 's are =.

5. ABD=CDB given, BD=DB identity, ADB=CBD given, ABDCDB. ASA=ASA,AB=CD corresponding sides of 's are =.

7. AC=BC given, ACD=BCD given, CD=CD identity, ACDBCD. SAS=SAS,A=B corresponding 's of 's are =.

9. BAE=DCE alternate interior 's of || lines are =, AB=CD given, ABE=CDE alternate interior 's of || lines are =, ABECDE. ASA=ASA, AE=CE corresponding sides of 's are =.

11. ABC=DCE corresponding 's of || lines are =, A=D give, AC=DE given, ABCDCE. AAS=AAS, BC=CE corresponding sides of 's are =.

13. AD=BC given, BAD=ABC given, AB=BA identity, ABDBAC. SAS=SAS, AC=BD corresponding sides of 's are =.

Section 2.5

1. 35

3. 7

5. 45

7. x=18,A=B=52,C=76

9. x=4,AB=24,AC=BC=21

11. x=1,y=4,AC=10

13. 125

Section 2.6

1. ABCFDE, SSS=SSS:AB,BC,AC of ABC=FD,DE,FE of FDE,x=30,y=70,z=80

3. ABDCDB, SSS=SSS:AB,BD,AD of ABD=CD,DB,CB of CBD,x=70,y=50,z=60

5. ABCEDC, SAS=SAS:AC,ACB,CB of ABC=EC,ECD,CD of EDC,x=8,y=60,z=56

7. ABCADC,ASA=ASA:BAC,AC,ACB of ABC=DAC,AC,ACD of ADC,x=3,y=4

9. AB=DE,BC=EF,AC=DF given, ABCDEF. SSS=SSS,A=D corresponding 's of 's are =.

11. AB=AD,BC=DC given, AC=AC identity, ABCADC. SSS=SSS, BAC=CAD corresponding 's of 's are =.

13. AE=CE given, AEB=CED vertical 's are =, EB=ED given, AEBCED SAS = SAS, AB = CD corresponding sides of \cong \triangle's are =.

Section 2.7

1. (1) \triangle ABC \cong \triangle DEF

(2) Hyp-Leg = Hyp-Leg: AB, BC of \triangle ABC = DE, EF of \triangle DEF

(3) x = 42, y = 48

3. Triangles cannot be proven congruent.

5. Triangles cannot be proven congruent.

7. (1) \triangle ABC \cong \triangle CDA

(2) AAS = AAS: \angle B, \angle BCA, CA of \triangle ABC = \angle D, \angle DAC, AC of \triangle CDA

(3) x = 25, y = 20

9. (1) \triangle ACD \cong \triangle BCD

(2) SAS = SAS: AD, \angle ADC, DC of \triangle ACD = BD, \angle BDC, DC of \triangle BCD

(3) x = 4

11. Triangles cannot be proven congruent.

13. Triangles cannot be proven congruent.

15. Triangles cannot be proven congruent.

17. OP = OP identity, OA = OB given, \triangle OAP \cong \triangle OBP Hyp-Leg = Hyp-Leg, AP = BP corresponding sides of \cong \triangle's are =.

19. AB = CD, AD = CB given, BD = DB identity, \triangle ABD \cong \triangle CDB SSS = SSS, \angle A = \angle C corresponding \angle's of \cong \triangle's are =.

21. AD = BD given, \angle ADC = \angle BDC = 90^{\circ} given AB \perp CD, CD = CD identity, \triangle ACD \cong \triangle BCD. SAS = SAS, \angle A = \angle B corresponding \angle's of \cong \triangle's are =.

Section 3.1

1. w = 40, y = 140, r = 4, s = 8

3. w = 35, x = 25, y = 120, z = 35

5. x = 130, y = 50, z = 130

7. x = 70, \angle A = 70^{\circ}, \angle B = 110^{\circ}, \angle C = 70^{\circ}, \angle D = 110^{\circ}

9. x = 25, y = 20, AC = 40, BD = 50

11. x = 2, AB = CD = 4 or x = 3, AB = CD = 9

13. x = 4, y = 1, AB = CD = 7, AD = BC = 3

15. x = 4, y = 2, AC = 16, BD = 12

17. x = 20, y = 10, \angle A = 40^{\circ}, \angle B = 140^{\circ}, \angle C = 40^{\circ}, \angle D = 140^{\circ}

Section 3.2

1. w = 50, x = 40, y = 50, z = 50

3. x = 30, y = 60

5. x = 4, y = 4, z = 4, AC = 8, BD = 8

7. x = 40, y = 40, z = 100

9. 1

11. x = y = z = 45

13. x = 60, y = z = 120

15. x = 135, y = 100

17. w = x = 50, y = 130, z = 50

19. 5

Section 4.1

1. 1

3. 12

5. 21

7. 20

9. 6

11. 1 or 6

Section 4.2

1. \triangle ABC \sim \triangle FED

3. \triangle ABC \sim \triangle DFE

5. \triangle ABC \sim \triangle DBE

7. 6

9. 7

11. 1

13. 5

15. 6

17. x = 6, y = 1.5

19. 15

21. x = 4.5, y = 1.5, z = 15

23. 100 feet

Section 4.3

1. 5

3. 1.5

5. 4

Section 4.4

1. 10

3. 8

5. \sqrt{2}

7. \sqrt{3}

9. 3\sqrt{2}

11. x = 6, BC = 6, AC = 8, AB = 10

13. x = 17, PR = 8, QR = 15, PQ = 17

15. 2\sqrt{2}

17. x = 3, AB = 16

19. x = 7, AC = 30, BD = 16

21. x = 8, y = 6

23. x = 5, AB = 12, BD = 13

25. yes

27. no

29. no

31. 24 feet

33. no

Section 4.5

1. x = 3\sqrt{3}, y = 6

3. x = 5, y = 5\sqrt{3}

5. x = \sqrt{3}, y = 2\sqrt{3}

7. x = 3, y = 3\sqrt{2}

9. x = y = 5\sqrt{2}

11. 10\sqrt{2}

13. 3\sqrt{2}

15. x = 8, y = 4\sqrt{3}

17. x = y = (5\sqrt{2})/2

19. x = 3, y = 3\sqrt{3}

21. x = 5\sqrt{3}, AB = 20

23. x = 3, y = 6

25. AC = 8, BD = 8\sqrt{3}

Section 4.6

1. 4

3. \sqrt{3}

5. 2\sqrt{2}

Section 5.1

1. \dfrac{12}{13}, \dfrac{5}{13}, \dfrac{12}{5}, \dfrac{5}{13}, \dfrac{12}{13}, \dfrac{5}{12}

3. \dfrac{8}{17}, \dfrac{15}{17}, \dfrac{8}{15}, \dfrac{15}{17}, \dfrac{8}{17}, \dfrac{15}{8}

5. \dfrac{1}{2}, \dfrac{\sqrt{3}}{2}, \dfrac{\sqrt{3}}{3}, \dfrac{\sqrt{3}}{2}, \dfrac{1}{2}, \sqrt{3}

7. \dfrac{\sqrt{2}}{2}, \dfrac{\sqrt{2}}{2}, 1, \dfrac{\sqrt{2}}{2}, \dfrac{\sqrt{2}}{2}, 1

9. \dfrac{\sqrt{3}}{2}, \dfrac{1}{2}, \sqrt{3}, \dfrac{1}{2}, \dfrac{\sqrt{3}}{2}, \dfrac{\sqrt{3}}{3}

11. \dfrac{2}{3}, \dfrac{\sqrt{5}}{3}, \dfrac{2\sqrt{5}}{5}, \dfrac{\sqrt{5}}{3}, \dfrac{2}{3}, \dfrac{\sqrt{5}}{2}.

13. \dfrac{1}{2}, \dfrac{\sqrt{3}}{2}, \dfrac{\sqrt{3}}{3}, \dfrac{\sqrt{3}}{2}, \dfrac{1}{2}, \sqrt{3}

15. \dfrac{3}{5}, \dfrac{4}{3}

17. \dfrac{1}{2}, \dfrac{\sqrt{3}}{3}

19. \dfrac{3\sqrt{10}}{10}, \dfrac{\sqrt{10}}{10}

Section 5.2

1. .1736

3. .1736

5. 1.0000

7. .3090

9. 1.1918

11. 6.4

13. 7.7

15. 11.9

17. 8.4

19. 44.8

21. 7.8

23. 20.5

25. 14.5

27. 7.3

29. 4.8

31. 42^{\circ}

33. 37^{\circ}

35. 56^{\circ}

37. 48^{\circ}

39. 4.6

41. x = 4.6, y = 7.7

43. 7.8

45. x = 8.2, y = 26.5

Section 5.3

1. 50.3 feet

3. 5759 feet

5. 1^{\circ}

7. 18.8 feet

Section 6.1

1. A = 12, P = 16

3. A = 49, P = 28

5. A = 3, P = 4\sqrt{5}

7. A = 120, P = 46

9. A = 48, P = 28

11. A = 25\sqrt{3}, P = 10 + 10\sqrt{3}

13. A = 50, P = 20\sqrt{2}

15. 4

17. 4

19. 48000 square feet

21. 296

23. 450

25. 1800 pounds

Section 6.2

1. A = 240, P = 66

3. A = 36, P = 28

5. A = 96.4, P = 50

7. A = 10, P = 10 + 4\sqrt{2}

9. 7

11. 4

13. x = 8, y = 5

Section 6.3

1. 60

3. 10

5. 11.5

7. A = 6, P = 12

9. A = 108, P = 54

11. A = 44, P = 28 + 4\sqrt{5}

13. A = 60, P = 40

15. A = 2, P = 4 + 2\sqrt{2}

17. A = 16\sqrt{3}, P = 24

19. A = 42.0, P = 31.4

21. 5

23. 4

Section 6.4

1. 42

3. A = 96, P = 40

5. A = 24, P = 20

7. A = 32\sqrt{3}, P = 32

9. 167.8

Section 6.5

1. 40

3. A = 36, P = 28

5. A = 32, P = 21 + \sqrt{17}

7. A = 44, P = 32

9. A = 50 + 25\sqrt{3}, P = 40 + 10\sqrt{3}

11. A = 375\sqrt{3}, P = 95 + 5\sqrt{21}

13. A = 269.2, P = 84.9

15. 7

Section 7.1

1. x = y = z = 60, r = 3

3. x = 72, y = z = 54, r = 7

5. x = 90, y = z = 45, r = 5

7. a = 27.5, P = 200, A = 2752.8

9. a = 17.3, P = 120, A = 1039.2

11. a = 30.8, P = 200, A = 3077.7

13. a = 16.2, P = 117.6, A = 951.1

15. a = 8.7, P = 60, A = 259.8

17. a = 9.5, P = 61.8, A = 293.9

Section 7.2

1. r = 20, d = 40

3. 30

5. 6

7. r = 15, d = 30

9. r = 10, d = 20

11. AB = 12, CD = 16

Section 7.3

1. 15

3. 80

5. x = 40, \angle O = 125^{\circ}, \angle P = 55^{\circ}

7. x = 25, y = 24

9. 10

11. 7

13. 36

15. 40

Section 7.4

1. \widehat{AB} \stackrel{\circ}{=} 60^{\circ}, \widehat{ACB} \stackrel{\circ}{=} 300^{\circ}

3. \widehat{AB} \stackrel{\circ}{=} 80^{\circ}, \widehat{ACB} \stackrel{\circ}{=} 280^{\circ}

5. x = 80, y = 70, z = 90

7. x = 60, y = 60, z = 60

9. x = 35, y = 70, z = 70

11. 130

13. 50

15. 60

17. 70

19. 50

21. 90

23. 12

25. 40

27. x = 50, y = z = 25

29. 70

31. x = 45, y = 45, z = 90

33. 35

35. x =. 70, y = 40, z = 30

37. 80

39. x = 45, y = 15, z = 60

41. x = 30, y = 50, z = 80

43. 30

45. 70

Section 7.5

1. 31.4

3. 62.8

5. 12.56, 25.12

7. 40.82

9. 8.37

11. 52.3

13. 6.28

15. \widehat{AB} = 3.925, \widehat{CD} = 7.85

17. 39.1

19. 94.2

21. 62.8

23. r = 50, d = 100

25. 43.96 inches

27. 7907.6 miles

Section 7.6

1. 3.14

3. 12.56

5. 78.5

7. 1256

9. 113.04

11. 157

13. 62.8

15. (200\pi/3) - 100\sqrt{3}

17. 25\pi - 50

19. 100\pi - 200

21. 100 - 25\pi

23. 200 + 25\pi

25. 21 \pi

27. 50\pi

29. 100 - 25\pi

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