PQ

(1)

8.1 Basic Geometric Figures

1. ray

2. segment 3. line

4. point 5. angle 6. plane 7. plane 8. ray 9. angle

10. point

11. PQ →

12. MN ←→

, or NM ←→

13. CD, or DC

(2)

Section 8.1

15.

16. 17. 18.

19.

20. E

21. AB BC AC, ,

22. XY

←→

, YZ

←→

, XZ

←→

23. YZ

→

, YX

→

24. XY

←→

, XZ

←→

25. Y

(3)

Section 8.1

28. ∠_JKL_,∠_LKM_,∠_JKM 29. 25°, acute

30. 90°, right

31. 180°, straight 32. 60°, acute 33. 130°, obtuse 34. 70°, acute 35. 35°

36. 128°

37. 70° 38. 55° 39. 110° 40. 90° 41. 180° 42. 90°

43. AB

→

and AC

→

(4)

Section 8.1

44. AB

←→

and CD

←→

; same line 45. ∠_V_and∠_UVW_{; same}

angle

46. CD and DC; same segment 47. XY

and XZ

; same ray 48. 2 hr. 45 min.

49. 6 hr. 25 min. 50. 2 hr. 44 min. 51. 16 hr.

52. 7 hr. 41 min. 53. EST

(5)

8.2 Pairs of Angles

1. 60°

2. 62°

3. 25°

4. 38°

5. 77°

6. 23°

7. neither

8. perpendicular

9. parallel

10. neither

11. perpendicular

12. parallel

13. acute

14. obtuse

15. right

16. straight

17. 130°

(6)

Section 8.2

19. 40°

20. 147°

21. 90°

22. 13°

23.

24.

25.

(7)

Section 8.2

27.

28.

29.

30.

(8)

Section 8.2

32. supplementary

33. supplementary

34. supplementary

35. corresponding

36. corresponding

37. corresponding

38. vertical

39. vertical

40. vertical

41. 148°

42. 32°

43. 148°

44. 116°

45. 64°

46. 64°

47. 64°

48. 64°

49. 116°

50. 116°

(9)

Section 8.2

52. sometimes

53. sometimes

54. always

55. 57°

56. 123°

57. 123°

58. 123°

59. 57°

60. 5

61. 230

62. 100

63. <

64. >

65. <

66. 982 g

67. 14.0 m

68. 1, 2, 0, 3, 5

(10)

Problem Solving 8—Work Backwards

1. Divide by 3 and subtract 10. 2. Subtract 8 and multiply by 12. 3. 1: n = 6; 2: n = 120

4. 28 cookies in each batch 5. $42

6. 4:05 PM 7. 3 hr.

(11)

8.3 Polygons

1. heptagon

2. regular pentagon 3. triangle

4. decagon 5. octagon

6. quadrilateral or rectangle 7. b

8. d 9. c

(12)

Section 8.3

19. false 20. false 21. 104° 22. 32° 23. 50° 24. 37° 25. 87° 26. 90° 27. 89°

(13)

Section 8.3

37. 1,440° 38. 3,240° 39. 60° 40. 90° 41. 120° 42. 144°

43. The sum of the angle

measures increases with the number of sides. Thus, the more sides a regular

polygon has, the more it looks like a circle.

(14)

Section 8.3

47.

48. b 49. c 50. b 51. a

52. 17.775

53. 76.34

(15)

8.4 Triangles and Quadrilaterals

1. F 2. T 3. T 4. F 5. T 6. F 7. F 8. T 9. T

10. F 11. right 12. acute 13. obtuse 14. acute 15. obtuse 16. right

(16)

Section 8.4

19. scalene 20. scalene 21. isosceles 22. equilateral

23. obtuse, scalene 24. right, isosceles 25. acute, equilateral

26.

(17)

Section 8.4

28.

29. square 30. rhombus 31. trapezoid 32. rectangle

33. parallelogram 34. trapezoid

35. a, c, d, e, f

36. a, b, c, d, e, f 37. c

38. a, c, e, f 39. a, c

(18)

Section 8.4

42.

43.

44.

45. no; If a quadrilateral had four acute angles, the sum of its angles would be less than 360°.

46. triangles, squares, parallelograms

(19)

Section 8.4

50. 26°, acute 51. 117°, obtuse 52. 92°, obtuse 53. 38°, acute 54. 432

55. 11 2

56. 9,240 57. 2

1

4

58. N O

(20)

8.5 Pythagorean Theorem

1. 20

2. 15

3. 29

4. 89

5. 34

6. 13

7. 5

8. 10

9. 65

10. 45

11. 25

12. 370

13. 85

14. 181

15. 17

16. 160

17. 346

(21)

Section 8.5

19. 250

20. 433

21. 12

22. 3

23. 108

24. 171

25. 7

26. 12

27. 9

28. 128

29. 9

30. 231

31. 10 ft.

32. 5 ft.

33. 147 _≈ 12.1 m

34. 200 _≈ 14.1 in.

35. 10.8 in.

36. d

37. b

(22)

Section 8.5

39. e

40. c

41. 19°

42. 54°

43. 66.3°

44. vertical

45. corresponding

46. corresponding

47. supplementary

48. (3 ×₁₀0_{) +}

1 1 7 10   ×     + 2 1 2 10   ×    

49. 4 1₂ 10

 

×

 

  + 3 1 5 10   ×     + 4 1 3 10   ×    

50. (7 ×₁₀2_{) + ( 6}×₁₀0_{) +}

1 1 9 10   ×  

  + 3

(23)

8.6 Perimeter

1. 24 m 2. 28 cm 3. 16.7 m 4. 46.3 cm 5. 23.6 m 6. 28 cm 7. 47.4 ft. 8. 57.2 m 9. 43.5 in.

(24)

Section 8.6

19. 46 cm 20. 22 ft. 21. 61 m 22. 40.8 in. 23. 62.8 mm 24. 44.2 cm 25. 15 m 26. 108 mm 27. 92 cm

28. 7.2 m 29. 14 cm 30. 8 m 31. 336 ft. 32. 42 posts 33. 24 ft.

34. l = 16 m; w = 8 m 35. 46 in.

36. 11

(25)

Section 8.6

37. 31.5 in. 38. 720° 39. 2,520° 40. 1,260° 41. 110 42. 100

43. 72 44. 20

45. pentagon 46. heptagon

(26)

8.7 Circles and Circumference

1. true 2. false 3. false 4. true 5. center 6. diameter

7. central angle 8. radius

9. arc

10. chord 11. point M

12. MO MP MN, , 13. NO

14. NO QR,

15. Answers may vary. _, _,

QN NP PO

(27)

Section 8.7

18. 6.5 cm 19. 5 cm 20. 115° 21. 5 cm 22. 10 cm 23. 10 cm 24. 65° 25. 15.7 m 26. 50.24 mm

(28)

Section 8.7

36. 46.47 in. 37. 22 cm 38. 176 m 39. 110 in. 40. 33 ft.

41. isosceles

42. right

(29)

Section 8.7

48. 12.5 m 49. 1.75 cm 50. yes

51. no 52. yes

53. $41.02

54. $18

55. scalene, obtuse 56. isosceles, right 57. scalene, acute 58. 139°

(30)

8.8 Congruent Figures

1. AB ≅ EF

2. ∠_G ≅ ∠_I

3. ∆_JKL ≅ ∆_PRQ 4. ∠_D ≅ ∠_E

5. HI ≅ LM

6. ∆_ABC ≅ ∆_GHI 7. PR

8. NO

9. QP

10. ∠_M 11. ∠_R 12. ∠_O 13. EF

14. FG

15. DA

(31)

Section 8.8

17. ∠_E 18. ∠_F 19. ∠_D 20. ∠_C 21. 30° 22. Z

23. T

24. 3 25. TR

26. YZ

27. 5 in. 28. M

29. 90° 30. ON

31. 118° 32. 9 in. 33. VU

(32)

Section 8.8

35. true 36. false

37. ∆_ABE ≅ ∆_BCE ≅ ∆_CDE ≅ ∆_DAE

∆_ABC ≅ ∆_BCD ≅ ∆_CDA ≅

∆_DAB

38. ∆_ACJ ≅ ∆_ADH ≅ ∆_BEI ≅ ∆_BDF ≅ ∆_CEG

39. ∆_ABF ≅ ∆_BAH ≅ ∆_BCG ≅ ∆_CBI ≅ ∆_CDH ≅ ∆_DCJ ≅

∆_DEI ≅ ∆_EDF ≅ ∆_EAJ ≅

∆_AEG

40. 5 different sizes; any of the nine congruent to ∆_ABC; any of the four congruent to ∆_{ABD; any of the four}

congruent to ∆_{ABG; any of} the nine congruent to

(33)

Section 8.8

41. No; the triangles have different bases.

42. 128 43. 1,372 44. 63 45. 20 in. 46. 12 cm 47. 17 ft.

48. 5 4 15

49. 15 6

50. 1013 24

(34)

8.9 Similar Figures

1. similar 2. congruent 3. congruent 4. neither 5. similar 6. similar 7. congruent 8. neither 9. neither

(35)

Section 8.9

19. 1 : 2 20. 8 : 5 21. x = 15 22. x = 2 23. x = 35 24. x = 7 25. x = 57 26. x = 12 27. x = 10.5

28. x = 16.5 29. x = 13 30. x = 78 31. 3 : 2

32. 8 in. ×_{12 in.}

(36)

Section 8.9

34. 12 ft. 35. no 36. yes 37. no

42. 39.1 m 43. 28 in. 44. 72.8 cm

(37)

Math and Scripture 8

1. Answers will vary. 2. Answers will vary. 3. 30 cubits, 45 ft.

4. 9.5 cubits (or 9.6 cubits), 14.3 ft. (or 14.4 ft.)

5. 10 cubits, 15 ft.

6. 9.5 cubits (or 9.6 cubits), 14.3 ft. (or 14.4 ft.)

7. within a tenth of a cubit 8. weigh it

9. 5,745 gal.

(38)

Chapter 8 Review

1. point

2. line

3. plane

4. GH ←→

5. ∠_IJK_, ∠_KJI_{, or} ∠_J

6. LM

7. 35°

8. 102°

9. 69°

10. 33°

11. neither

12. perpendicular

13. supplementary

14. vertical

15. corresponding

16. hexagon

17. pentagon, regular

(39)

Chapter 8 Review

19. 35°

20. 35°

21. 540°

22. 3,060°

23. right, scalene

24. obtuse, scalene

25. acute, equilateral

26. trapezoid

27. rhombus

28. parallelogram

29. 115°

30. x = 13

31. x = 421

32. x = 312

33. 40 cm

34. 31.8 m

35. 42.4 cm

36. 13 in.

37. radius

(40)

Chapter 8 Review

39. chord

40. 12.56 m

41. 56.52 cm

42. 44 ft.

43. XY

44. C

45. YZ

46. B

47. congruent

48. neither

49. similar

50. x = 3

51. x = 55

52. The brim of the molten sea was a handbreadth wide, which shows that the

circumference and diameter given are not for the same circle. This affects the