Solutions Manual - Anoka-Hennepin School District 11

Solutions Manual

This booklet is provided in Glencoe Geometry Answer Key Maker (0-07-860264-5).

Also provided are solutions for problems in the Prerequisite Skills, Extra Practice,

and Mixed Problem Solving sections.

Copyright ? by The McGraw-Hill Companies, Inc. All rights reserved.

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material contained herein on the condition that such material be reproduced only

for classroom use; be provided to students, teacher, and families without charge;

and be used solely in conjunction with Glencoe Geometry. Any other reproduction,

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8787 Orion Place

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ISBN: 0-07-860204-1

1 2 3 4 5 6 7 8 9 10 009 12 11 10 09 08 07 06 05 04 03

Geometry

Solutions Manual

CONTENTS

Chapter 1 Points, Lines, Planes, and Angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Chapter 2 Reasoning and Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 24

Chapter 3 Parallel and Perpendicular Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Chapter 4 Congruent Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Chapter 5 Relationships in Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120

Chapter 6 Proportions and Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .151

Chapter 7 Right Triangles and Trigonometry. . . . . . . . . . . . . . . . . . . . . . . . . . .. 189

Chapter 8 Quadrilaterals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

Chapter 9 Transformations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

Chapter 10 Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

Chapter 11 Areas of Polygons and Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383

Chapter 12 Surface Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 411

Chapter 13 Volume¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­...447

Prerequisite Skills ¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­477

Extra Practice¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­502

Mixed Problem Solving and Proof¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­567

Chapter 1 Points, Lines, Planes, and Angles

2. See students¡¯ work; sample answer: Two lines

intersect at a point.

3. Micha; the points must be noncollinear to

determine a plane.

4. Sample answers: line p; plane R

5. Sample answer:

y

Page 5 Getting Started

1¨C4.

y

D( 1, 2)

B(4, 0)

x

O

A(3, 2)

W

C( 4, 4)

x

O

X



3

6

3


5.
3

4  8  8  8





1



9

8  18

Z

Y

5


37

4


1


1







6. 2


16  5 8 ? 16  8

37

82








?


16  16

6.

r

P

11


9


7


?


16 ?7 16

s

Q

14



9





9


7.
7

8  16 ? 16  16

5


?


16

23

15


1





7







8. 11
1

2  9 16 ? 2  16

18


4

15


1




?


16  16

33





1


?


16  2 16

7. There are six planes: plane ABC, plane AGE,

plane CDE, plane BCD, plane FAB, and plane

DEF.

8. A, K, B or B, J, C

9. No; A, C, and J lie in plane ABC, but D does not.

10. line

11. point

12. plane

9. 2  17  15

10. 23  (14)? 23  14

 37

11. [7  (2)]2? (7  2)2

 (5)2  25

12. 92  132? 81  169

 250

13. P? 4s

 4(5)  20

The perimeter is 20 in.

14. P? 2
 2w




? 2(6)  2 2
1

2

Pages 9¨C11

n

R




Sample answer: PR

Yes, it intersects both

lines are extended.

19. (D, 9)

21.

B




? 12  5  17

The perimeter is 17 ft.

15. P? 2
 2w

 2(4.8)  2(7.5)

 9.6  15  24.6

The perimeter is 24.6 m.

1-1

Practice and Apply

13.

15.

17.

18.

W

14. F

16. W

m and n when all three

20. Charlotte

Q

A

22.

R

W

T

23. Sample answer:

Points, Lines, and Planes

y

Page 8 Geometry Activity

R

S

Z

1. no

2. no




3. On CD; see students¡¯ work.

4. See students¡¯ work.

x

O

Q

Page 9 Check for Understanding

1. point, line, plane

1

Chapter 1

24. Sample answer:

36. Sample answer: points E, A, and B are coplanar,

but points E, A, B, and C are not.

37.


AC

38. point

39. lines

40. plane

41. plane

42. two planes intersecting in a line

43. point

44. intersecting lines

45. point

46. line

47.

y

R

C

P

D

S

x

O

25.

a

b

c

26.

48.

a

b

F

V

c

27.

s

C

49. See students¡¯ work.

50. Sample answer: the image is rotated so that the

front or back plane is not angled.

51. Sample answer:

r

D

M

s

28.

A

B

C

52. See picture.

53. vertical

54. Sample answer: the paths flown by airplanes

flying in formation

55. Sample answer: Chairs wobble because all four

legs do not touch the floor at the same time.

Answers should include the following.

? The ends of the legs represent points. If all points

lie in the same plane, the chair will not wobble.

? Because it only takes three points to determine a

plane, a chair with three legs will never wobble.

56. C; Three lines intersect in a maximum of three

points. The fourth line can cross the other three

lines only one time each, adding three points to

the figure. For example,

29. points that seem collinear; sample answer:

(0, 2), (1, 3), (2, 4), (3, 5)

y

O

x

30. There are five planes: plane ABC, plane BCE,

plane ABE, plane ADE, and plane CDE.

31. 1; There is exactly one plane through any three

noncollinear points.

32. E, F, C

33. Because A and B determine a line, add point G


.

anywhere on AB

34. E, F

35. A, B, C, D or E, F, C, B

Chapter 1

2

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