Answers to Odd Numbered Problems

Section 1.1

1. 6

3. $x = 9$, $AC = 24$.

5. 15

7. 3

Section 1.2

1. $\angle CBD$ or $\angle DBC$

3. $\angle AED$ or $\angle DEA$

5. $\angle ABC$ or $\angle CBA$

7. $70^{\circ}$

9. $x = 130^{\circ}$, $y = 50^{\circ}$

11. $x = 30^{\circ}$, $y = 60^{\circ}$

13. $\angle A = 60^{\circ}$, $\angle B = 50^{\circ}$, $\angle C = 70^{\circ}$

15. $\angle A = 110^{\circ}$, $\angle B = 80^{\circ}$, $\angle C = 70^{\circ}$, $\angle D = 100^{\circ}$

17.

19.

21.

23.

25. $35^{\circ}$

27. $30^{\circ}$

Section 1.3

1. (a) $53^{\circ}$ (b) $45^{\circ}$ (c) $37^{\circ}$ (d) $30^{\circ}$

3. $15^{\circ}$

5. $30^{\circ}$

7. (a) $150^{\circ}$ (b) $143^{\circ}$ (c) $90^{\circ}$ (d) $60^{\circ}$

9. $30^{\circ}$

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. $45^{\circ}$

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: $\angle ABD$ & $\angle CDB - AB||CD$; $\angle ADB$ & $\angle CBD - AD||BC$

21. corresponding: $\angle BAC$ & $\angle EDC - AB||DE$; $\angle ABC$ & $\angle DEC - AB||DE$

23. interior on same side of transversal: $\angle BAD$ & $\angle CDA - AB||CD$; $\angle ABC$ & $\angle DCB - AB||CD$

25. alternate interior: $\angle BAC$ & $\angle DCA - AB|| DE$; $\angle ABC$ & $\angle ECB - AB||DE$

27. $65^{\circ}$

Section 1.5

1. $85^{\circ}$

3. $37^{\circ}$

5. $60^{\circ}$

7. 30

9. 6

11. 120

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

15. $65^{\circ}$

17. 8

19. 24

21. $720^{\circ}$

23. $60^{\circ}$

25. $108^{\circ}$

Section 1.6

1. 2/3

3. 6

5. $x = 1, AB = 2$

7. $x = 9, \angle ACB = 90^{\circ}$

9. $\dfrac{25x + 11}{6}, \dfrac{37}{2}$

11. 5

Section 2.1

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

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

5. $\triangle PQR \cong \triangle STU$

7. $\triangle ABC \cong \triangle ABD$

9. $\triangle ABD \cong \triangle CDB$

Section 2.2

1. $BC = 1.7$, $\angle = 30^{\circ}$, $\angle C = 90^{\circ}$

3. $BC = 1.95, \angle B = 99^{\circ}, \angle C = 41^{\circ}$

5. $\angle B$

7. $\angle D$

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

(2) $\triangle ABC \cong \triangle DEF$

(3) $x = 65, y = 45$

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

(2) $\triangle ABC \cong \triangle EFD$

(3) $x = 40, y = 50$

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

(2) $\triangle ABC \cong \triangle EDF$

(3) $x = 8$

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

(2) $\triangle ABC \cong \triangle EDF$

(3) $x = 20, y = 30$

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

(2) $\triangle ABC \cong \triangle CDA$

(3) $x = 22$

19. (1) $AC, \angle ACD, CD$ of $\triangle ACD = BC, \angle BCD, CD$ of $\triangle BCD$

(2) $\triangle ACD \cong \triangle BCD$

(3) $x = 50$

21. (1) $AD, \angle ADC, DC$ of $\triangle ACD = BD, \angle BDC, DC$ of $\triangle BCD$

(2) $\triangle ACD \cong \triangle BCD$

(3) $x = 2$

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

(2) $\triangle ABC \cong \triangle EDC$

(3) $x = 20, y = 10$

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

(2) $\triangle ABC \cong \triangle EDC$

(3) $x = 70$

Section 2.3

1. $BC = 1.9, AC = 2.3, \angle C = 90^{\circ}$

3. $BC = 2.3, AC = 1.9, \angle C = 90^{\circ}$

5. $AB$

7. $DF$

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

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

(3) $x = 5, y = 6$

11. (1) $\triangle RST \cong \triangle UWV$

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

(3) $x = 7, y = 6$

13. (1) $\triangle ABD \cong \triangle CDB$

(2) $ASA = ASA: \angle B, BD, \angle D$ of $\triangle ABD = \angle D, DB, \angle B$ of $\triangle CDB$

(3) $x = 30, y = 25$

15. (1) $\triangle ABC \cong \triangle EDC$

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

(3) $x = 11, y = 9$

17. (1) $\triangle ACD \cong \triangle BCD$

(2) $AAS = AAS: \angle A, \angle ACD, CD$ of $\triangle ACD = \angle B, \angle BCD, CD$ of $\triangle BCD$

(3) $x = 5, y = 5$

19. (1) $\triangle ABC \cong \triangle EDC$

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

(3) $x = 2, y = 3$

21. (1) $\triangle ABC \cong \triangle EDF$

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

(3) $x = 2, y = 3$

23. $\triangle PTB \cong \triangle STB$, $ASA = ASA: \angle PTB, TB, \angle TBP$ of $\triangle PTB = \angle STB, TB, \angle TBS$ of $\triangle STB$. $SB = PB = 5, SP = SB + BP = 5 + 5 = 10$.

25. $\triangle DEC \cong \triangle BAC$, $ASA = ASA: \angle E, EC, \angle ECD$ of $\triangle DEC = \angle A, AC, \angle ACB$ of $\triangle BAC. AB = ED = 7$.

Section 2.4

1. $\angle A = \angle D$ given, $AB = DE$ given, $\angle B = \angle E$ given, $\triangle ABC \cong \triangle EDF$. (ASA = ASA, AC = DF\) corresponding sides of $\cong \triangle$'s are =.

3. $AC = EC$ given, $\angle ACB = \angle ECD$ vertical $\angle$'s, $BC = DC$ given, $\triangle ABC \cong \triangle EDC$. $SAS = SAS, AB = ED$ corresponding sides of $\cong \triangle$'s are =.

5. $\triangle ABD = \angle CDB$ given, $BD = DB$ identity, $\angle ADB = CBD$ given, $\triangle ABD \cong \triangle CDB$. $ASA = ASA, AB = CD$ corresponding sides of $\cong \triangle$'s are =.

7. $AC = BC$ given, $\angle ACD = \angle BCD$ given, $CD = CD$ identity, $\triangle ACD \cong \triangle BCD$. $SAS = SAS, \angle A = \angle B$ corresponding $\angle$'s of $\cong \triangle$'s are =.

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

11. $\angle ABC = \angle DCE$ corresponding $\angle$'s of $||$ lines are =, $\angle A = \angle D$ give, $AC = DE$ given, $\triangle ABC \cong \triangle DCE$. $AAS = AAS$, $BC = CE$ corresponding sides of $\cong \triangle$'s are =.

13. $AD = BC$ given, $\angle BAD = \angle ABC$ given, $AB = BA$ identity, $\triangle ABD \cong \triangle BAC$. $SAS = SAS$, $AC = BD$ corresponding sides of $\cong \triangle$'s are =.

Section 2.5

1. 35

3. 7

5. 45

7. $x = 18, \angle A = \angle B = 52^{\circ}, \angle C = 76^{\circ}$

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

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

13. 125

Section 2.6

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

3. $\triangle ABD \cong \triangle CDB$, $SSS = SSS: AB, BD, AD$ of $\triangle ABD = CD, DB, CB$ of $\triangle CBD, x = 70, y = 50, z = 60$

5. $\triangle ABC \cong \triangle EDC$, $SAS = SAS: AC, \angle ACB, CB$ of $\triangle ABC = EC, \angle ECD, CD$ of $\triangle EDC, x = 8, y = 60, z = 56$

7. $\triangle ABC \cong \triangle ADC, ASA = ASA: \angle BAC, AC, \angle ACB$ of $\triangle ABC = \angle DAC, AC, \angle ACD$ of $\triangle ADC, x = 3, y = 4$

9. $AB = DE, BC = EF, AC = DF$ given, $\triangle ABC \cong \triangle DEF$. $SSS = SSS, \angle A = \angle D$ corresponding $\angle$'s of $\cong \triangle$'s are =.

11. $AB = AD, BC = DC$ given, $AC = AC$ identity, $\triangle ABC \cong \triangle ADC$. $SSS = SSS$, $\angle BAC = \angle CAD$ corresponding $\angle$'s of $\cong \triangle$'s are =.

13. $AE = CE$ given, $\angle AEB = \angle CED$ vertical $\angle$'s are =, $EB = ED$ given, $\triangle AEB \cong \triangle CED$ $SAS = SAS$, $AB = CD$ 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. $100 - 25\pi$