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.
19.
21.
23.
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 & ∠CDB−AB||CD; ∠ADB & ∠CBD−AD||BC
21. corresponding: ∠BAC & ∠EDC−AB||DE; ∠ABC & ∠DEC−AB||DE
23. interior on same side of transversal: ∠BAD & ∠CDA−AB||CD; ∠ABC & ∠DCB−AB||CD
25. alternate interior: ∠BAC & ∠DCA−AB||DE; ∠ABC & ∠ECB−AB||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. △PQR≅△STU
7. △ABC≅△ABD
9. △ABD≅△CDB
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) △ABC≅△DEF
(3) x=65,y=45
11. (1) AB,∠B,BC of △ABC=EF,∠F,FD of △EFD
(2) △ABC≅△EFD
(3) x=40,y=50
13. (1) AB,∠B,BC of △ABC=ED,∠D,DF of △EDF
(2) △ABC≅△EDF
(3) x=8
15. (1) AB,∠B,BC of △ABC=ED,∠D,DF of △EDF
(2) △ABC≅△EDF
(3) x=20,y=30
17. (1) BA,∠A,AC of △ABC=DC,∠C,CA of △CDA
(2) △ABC≅△CDA
(3) x=22
19. (1) AC,∠ACD,CD of △ACD=BC,∠BCD,CD of △BCD
(2) △ACD≅△BCD
(3) x=50
21. (1) AD,∠ADC,DC of △ACD=BD,∠BDC,DC of △BCD
(2) △ACD≅△BCD
(3) x=2
23. (1) BC,∠BCA,CA of △ABC=DC,∠DCE,CE of △EDC
(2) △ABC≅△EDC
(3) x=20,y=10
25. (1) AC,∠ACB,CB of △ABC=EC,∠ECD,CD of △EDC
(2) △ABC≅△EDC
(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) △ABC≅△DEF
(2) ASA=ASA: ∠A,AB,∠B of △ABC=∠D,DE,∠E of △DEF
(3) x=5,y=6
11. (1) △RST≅△UWV
(2) AAS=AAS:∠T,∠R,RS of △RST=∠V,∠U,UW of △UWV
(3) x=7,y=6
13. (1) △ABD≅△CDB
(2) ASA=ASA:∠B,BD,∠D of △ABD=∠D,DB,∠B of △CDB
(3) x=30,y=25
15. (1) △ABC≅△EDC
(2) ASA=ASA:∠A,AC,∠ACB of △ABC=∠E,EC,∠ECD of △EDC
(3) x=11,y=9
17. (1) △ACD≅△BCD
(2) AAS=AAS:∠A,∠ACD,CD of △ACD=∠B,∠BCD,CD of △BCD
(3) x=5,y=5
19. (1) △ABC≅△EDC
(2) ASA=ASA:∠B,BC,∠BCA of △ABC=∠D,DC,∠DCE of △EDC
(3) x=2,y=3
21. (1) △ABC≅△EDF
(2) ASA=ASA:∠B,BC,∠C of △ABC=∠D,DF,∠F of △EDF
(3) x=2,y=3
23. △PTB≅△STB, ASA=ASA:∠PTB,TB,∠TBP of △PTB=∠STB,TB,∠TBS of △STB. SB=PB=5,SP=SB+BP=5+5=10.
25. △DEC≅△BAC, 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, △ABC≅△EDF. (ASA = ASA, AC = DF\) corresponding sides of ≅△'s are =.
3. AC=EC given, ∠ACB=∠ECD vertical ∠'s, BC=DC given, △ABC≅△EDC. SAS=SAS,AB=ED corresponding sides of ≅△'s are =.
5. △ABD=∠CDB given, BD=DB identity, ∠ADB=CBD given, △ABD≅△CDB. ASA=ASA,AB=CD corresponding sides of ≅△'s are =.
7. AC=BC given, ∠ACD=∠BCD given, CD=CD identity, △ACD≅△BCD. 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 =, △ABE≅△CDE. ASA=ASA, AE=CE corresponding sides of ≅△'s are =.
11. ∠ABC=∠DCE corresponding ∠'s of || lines are =, ∠A=∠D give, AC=DE given, △ABC≅△DCE. AAS=AAS, BC=CE corresponding sides of ≅△'s are =.
13. AD=BC given, ∠BAD=∠ABC given, AB=BA identity, △ABD≅△BAC. 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. △ABC≅△FDE, SSS=SSS:AB,BC,AC of △ABC=FD,DE,FE of △FDE,x=30,y=70,z=80
3. △ABD≅△CDB, SSS=SSS:AB,BD,AD of △ABD=CD,DB,CB of △CBD,x=70,y=50,z=60
5. △ABC≅△EDC, SAS=SAS:AC,∠ACB,CB of △ABC=EC,∠ECD,CD of △EDC,x=8,y=60,z=56
7. △ABC≅△ADC,ASA=ASA:∠BAC,AC,∠ACB of △ABC=∠DAC,AC,∠ACD of △ADC,x=3,y=4
9. AB=DE,BC=EF,AC=DF given, △ABC≅△DEF. SSS=SSS,∠A=∠D corresponding ∠'s of ≅△'s are =.
11. AB=AD,BC=DC given, AC=AC identity, △ABC≅△ADC. SSS=SSS, ∠BAC=∠CAD corresponding ∠'s of ≅△'s are =.
13. AE=CE given, ∠AEB=∠CED vertical ∠'s are =, EB=ED given, △AEB≅△CED 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