CHAPTER 8mrjaffe.net/GeomRef/unit8solutions.pdf · Chapter 8continued 8.1 Mixed Review (p. 464) 68. 69. 70. 71. 72. 73. and 74. and 75. and 76. Lesson 8.2 8.2 Guided Practice (p

CHAPTER 8

158 GeometryChapter 8 Worked-out Solution Key

Copyright © McDougal Littell Inc. All rights reserved.

Think & Discuss (p. 455)

1. Sample answer: pantographs, dilations, and projections

2. About 2 times larger. Measuring each fish from nose totail, the smaller fish is in., the larger in., so

Skill Review (p. 456)

1. 2.

3. 4.

5. 6.

Lesson 8.1

Activity (p. 457)

1. Sample answer:

2.

3. The ratio is about the same as the ratio.

4. Answers may vary.

5. No; if all the units of measure are the same, they do notaffect the ratio.

8.1 Guided Practice (p. 461)

1. means; extremes 2.

3. 4.

5. 6.

x � 6

x � 2�93�

x2

�93

2x

�39

8:104:5

x � 4

6x � 24

10x � 4x � 24

10x � 4�x � 6�

8:24:1

; 2:81:4

10

x � 6�

4x

2:1 36 in.:18 in.

3 �12 in.

1 :18 in.

wrist:thumbneck:wrist

5.75:2.523:10

; 12.5:5.75

50:23

�8 � 3�4 � 0

��11�4

�114

5 � 26 � ��1� �

37

2 � 04 � 0

�24

�12

22 � 18 � 20 � 31 � 91

13 � 11 � 7 � 312 � 10 � 2 � 6 � 32

2216 �

1216 �

116 � 1.83.

1716

1216

7. 8.

9.

8.1 Practice and Applications (pp. 461–464)

10. 11. 12.

13. 14. 15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25. 26.BDCF

�77

� 1ABCD

�23

20 oz4 lb

�20 oz

4 lb�16 oz1 lb �

�20 oz64 oz

�5

16

400 m0.5 km

�400 m

0.5 km�1000 m1 km �

�400 m500 m

�45

2 lb20 oz

�

2 lb�16 oz1 lb �

20 oz�

32 oz20 oz

�85

6 yd10 ft

�

6 yd� 3 ft1 yd�

10 ft�

18 ft10 ft

�95

2 mi3000 ft

�

2 mi�5280 ft1 mi �

3000 ft�

10,560 ft3000 ft

�8825

350 g1 kg

�350 g

1 kg�1000 g1 kg �

�350 g

1000 g�

720

60 cm1 m

�60 cm

1m�100 cm1 m �

�60 cm

100 cm�

35

3 ft12 in.

�

3 ft�12 in.1 ft �

12 in.�

36 in.12 in.

�31

12 in.2 ft

�12 in.

2ft �12 in.1 ft

�12 in.24 in.

�12

7.5 cm10 cm

�34

16 mm20 mm

�45

69

�23

2252

�1126

488

�61

1624

�23

x � 6

9x � 54

x

27�

29

b � �6 �2b � 12

2b � 4b � 12 z � 9.6 or 485

2b � 4�b � 3� 5z � 48

2

b � 3�

4b

58

�6z

Thumb 2.5 in.

Wrist 5.75 in.

Neck 12.5 in.

mcrbg-0801-sk.qxd 6-15-2001 3:31 PM Page 158

Geometry 159Chapter 8 Worked-out Solution Key


Chapter 8 continued

27. 28.

29.

31.

32.

33.

35.

37.

39.

x � 12

5x � 4x � 12

5x � 4�x � 3�

5

x � 3�

4x

c �7030

�73

30c � 70

305

�14c

z �17510

�352

z � 7�2510�

z7

�2510

7z

�1025

x �207

7x � 20

x4

�57

15�5� � � 75�; 19�5�� 95�2�5� � � 10�;

x � 5

36x � 180

2x � 15x � 19x � 180

7�15�� 105�4�15�� 60�;1�15�� 15�;

x � 15

12x � 180

1x � 4x � 7x � 180

2�6� � 12 ft5�6� � 30 ft;

x � 6

14x � 84

2�7x� � 84

2�5x� � 2�2x� � 84

CFAB

�72

BFAD

�119

41.

43.

45.

47.

49. Venus: ; Mars:

Jupiter: ; Pluto:

50. 51.

x � 121 lb

x � 46�10038 �

x

46�

10038

120 ft�12 in.1 ft � � 1440 in.

46x

�38

100

x � 10 lb x � 330 lb

100x � 980 100x � 33,040

x

140�

7100

x

140�

236100

x � 53 lb x � 126 lb

100x � 5320 10x � 1260

x

140�

38100

; x

140�

910

z � 21

2z � 42

2z � 6 � 36

2�z � 3� � 36

z � 3

12�

32

12

z � 3�

23

x �483

� 16

x � 6�83�

x6

�83

6x

�38

y � �485

�5y � 48

30y � 48 � 35y

6�5y � 8� � 35y

5y � 8

7�

5y6

z � 15

7z � 6z � 15

7z � 3�2z � 5�

7

2z � 5�

3z

30.

Since length must be positive

34.

36.

38.

40.

y � 6

�4y � �24

4y � 8y � 24

4y � 8�y � 3�

4

y � 3�

8y

d � 32

3d � 96

3

16�

6d

163

�d6

b �1210

�65

b � 4� 310�

b4

�3

10

4b

�103

y �7210

�365

10y � 72

y8

�9

10

3�3� � 9 cm4�3� � 12 cm;

x � 3.

x � ±3

x2 � 9

12x2 � 108

4x�3x� � 108

42.

44.

46.

48. Venus because is closest to 1.910

y � 25

5y � 125

5y � 35 � 160

5�y � 7� � 160

y � 7

40�

45

z �688

�172

8z � 68

28z � 8 � 20z � 60

4�7z � 2� � 10�2z � 6�

4

2z � 6�

107z � 2

x �8018

�409

18x � 80

30x � 80 � 12x

10�3x � 8� � 6�2x�

3x � 8

6�

2x10


Chapter 8 continued



52.

53.

54.

56.

57.

58.

UT � �819 � 3�91 RQ � �91

�UT� 2 � 819 �RQ� 2 � 91

�UT� 2 � 30 2 � 9 2 �RQ� 2 � 10 2 � 32

ST � 30

ST � 10�31� PR � 3

ST10

�31

3�PR� � 9

10ST

�13

PR9

�13

PQ � 13 ST � 39

PQ � �169 ST � �1521

PQ � �52 � 122 ST � �362 � 152

SU � 15

SU � 5�31� RQ � 12

SU5

�31

3�RQ� � 36

5

SU�

13

RQ36

�13

k �143

or 423

3k � 14

7k � 14 � 10k

7�k � 2� � 5�2k�

k � 2

2k�

57

j � 18

4j � 72

j

24�

34

x � 1.0 in.

1440x � 1470

144035

�42x

35

1440�

x42

35 in.

1440 in.�

x

3.5 ft�12 in.1 ft �

x � 2.6 in.

3780 � 1440x

35

1440�

x108

35 in.

1440 in.�

x

9 ft�12 in.1 ft �

59.

61.

62.

63. EF � y � 20;

64.

65. Let x � number of pounds of compost.

D

66.

67.

and

AC � x � 16 � 20 � 16 � 36

x � 20

�10x � �200

216 � 9x � x � 16

9�24 � x� � x � 16

24 � xx � 16

�19

AC � x � 16.CD � 24 � xLet BC � x, then

AB � 16

3�AB� � 48

AB24

�23

2�15�� 30�, 3�15�� 45�, 7�15�� 105� D

x � 15

12x � 180

2x � 3x � 7x � 180

x � 18 lb

5x � 90

53

�30 lb

x

b � 15

6b � 5b � 15

6b � 5�b � 3� GR � b � 3 � 15 � 3 � 18

b

b � 3�

56

GH � HR � b � 15;

y � 20

DF � y � 4 � 20 � 4 � 24 4y � 80

45

�16y

x � 8

AB � x � 2 � 8 � 2 � 10 3x � 24

AC � x � 8; 34

�6x

72 ft

6 in.� 1 ft12 in.�

�72 ft0.5 ft

�1441

12:1

72:6

6 ft�12 in.1 ft �: 6 in.

55.

m � 6

�m � �6

3m � 6 � 4m

3m � 6

m�

41

60.

x � 72 ft

0.5x � 36

x6

�6

0.5

x

6 ft�

6 ft

6 in.� 1 ft12 in.�




Chapter 8 continued

8.1 Mixed Review (p. 464)

68.

69.

70. 71.

72.

73. and

74. and

75. and

76.

Lesson 8.2


1. 2. 3. ; or 3

4. and

(cross product property)

The equations are equal, therefore the statement is true.

5. 6.

7.

8. use stripes as a height unit measure � 7 stripes13 stripes�.

713

;

x � 11.4 ft

1

1.9�

6x

x � 6

DE � 9 x � �36

2�DE� � 18 x2 � 36

23

�6

DE 3x

�x

12

15r � 6s 15r � 6s

15s

�6r

rs

�6

15

62

y � 5ax

�xb

y

x

1

�11�1

A�(3, �3)

B(6, �7)B�(�2, �7)

A(1, �3)

�112

, 1��12

, 312�

�1 � 22

, 4 � ��2�

2 ��2 � 12

, 3 � 4

2 ��3

12

, �112��1, �2�

�1 � 62

, 1 � ��4�

2 ��1 � 12

, 1 � ��5�

2 �

�1, 3��112

, 3��1 � 3

2,

5 � 12 ��2 � ��1�

2,

1 � 52 �

WV

m�U � m�V � 95�m�T � m�W � 65�

m�V � 95�

m�V � 85� � 180�

m�V � 20� � 65� � 180�

m�X � m�S � 20�


9. 10. 11.

12.

13. By Property of proportions 4, the statement is true.

14. If then by the reciprocal property.

The statement is false.

15. By Property of proportions 3, the statement is true.

16. Similarily,

Then and the statement

is true by the subtraction property of equality.

17. 18.

19. 20.

21. 22.

23. 24.

25. 26.

x �352

� 1712

�2x � �35

7x � 35 � 9x

7�x � 5� � 9x x �406

�203

� 623

79

�x

x � 5 6x � 40

7

7 � 2�

xx � 5

4x

�6

10

x � 9

6x � 54 x �18016

�454

� 1114

186

�x3

16x � 180

24 � 66

�x3

20x

�169

x � 5�3 x � 4�10

x � �75 x � �160

x2 � 75 x2 � 160

5x

�x

15 8x

�x

20

x � 4�5 x � 14

x � �80 x � �196

x2 � 80 x2 � 196

2x

�x

40 7x

�x

28

x � 8 x � 9

x � �64 x � �81

x2 � 64 x2 � 81

4x

�x

16 3x

�x

27

m12

�3n

1 �m12

� 1 �3n

1 �3n

.

3 � nn

�12 � m

12�

1212

�m12

� 1 �m12

.

43

�rp

34

�pr ,

x � yy

y � 1212

634

�3

17xy


Chapter 8 continued



27.

29. Using in. for the 30. Using in. for the

width length

31. 32.

33. 34.

35. Each side of the equation represents the slope of the linethrough two of the points. If the points are collinear, theslopes are the same.

36. Given

Cross product property

Division property of equality

Simplify.

37. Given

Addition property of equality

Inverse property of multiplication

Addition of fractions a � b

b�

c � dd

ab

�bb

�cd

�dd

ab

� 1 �cd

� 1

ab

�cd

ac

�bd

adcd

�bccd

ad � bc

ab

�cd

y � 23 x � 11

92 � 4y 2x � 22

20 � 4y � 72 2x � 2 � 20

20 � 4�y � 18� 2�x � 1� � 20

104

�y � 18

2 25

�4

x � 1

18 � 86 � 2

�y � 188 � 6

1 � ��1�1 � ��4� �

5 � 1x � 1

x � 11,380 rubles x � 198 hits

22.761

�x

500

x643

�0.3081.000

x � 38 � 40 feet x � 26 � 25 feet

x �161 �38

16� x �161 �26

16�

116

x �3816

116

x �2616

x ft

3816

in.�

1 ft116

in.

x ft2616

in.�

1 ft116

in.

3816

2616

x �14421

�487

� 667

�21x � �144

144 � 9x � 12x

9�16 � x� � 12x

16 � x

x�

129

38. 39.

40.

feet

Sample answer: Construct a ramp consisting of tworamps in opposite directions, each 18 ft long. The first

should be 3 ft high at its beginning and ft high at

its end, for a rise:run ratio of . The second would be

ft high at its beginning and at ground level at its end.

The second ramp would also have a rise:run ratio of .

41. The map distance is 42. The map distance is

about or inch. about or inches.

43. If the two sizes share a dimension, the shorter dimensionof A5 paper must be the longer dimension of A6 paper.That is, the length of A6 paper must be 148 mm. Let x bethe width of A6 paper; 148 is the geometric mean of xand 210.

44. If of the fish are tetras, then are not tetras, so

D

45. Sample answer:

C

W � 3�3� � 9 games

L � 3

�2L � �6

3L � 6 � 5L

W � 6 � 5L

W � 6

L�

51

W � 3L

WL

�31

24 78

23

� 14.

78

18

x � 104 mm

210x � 21,904

x

148�

148210

x � 838

miles x � 212

miles

x �54

�6.7� x �38

�6.7�

x mi

114

in.�

6.7 mi1 in.

x mi38

in.�

6.7 mi1 in.

114

2016

38

616

112

112

112

112

x � 36

1

12�

3x

x �5

12�

54

� 114

ft

x � 24 ft 12x � 15

1

12�

2x

112

�x

1528.

x � 9

4x � 36

4x � 24 � 60

4�x � 6� � 60

x � 6

6�

104

x � 6

6�

4 � 64




Chapter 8 continued

46. a.

b.

So 2 is the geometric meanof and .

c.


47. 48.

49. 50.

51.

52.

53.

54.

55.

56.

57. A regular pentagon has 5 lines of symmetry (one fromeach vertex to the midpoint of the opposite side) androtational symmetries of and clockwise andcounterclockwise, about the center of the pentagon.

Developing Concepts Activity (p. 472)

Exploring the Concept

1. Photo 1: 4.2 cm; photo 2: 3.0 cm

2. 3. Both have measure .

4.30�

30�� 1

30�4.23.0

� 1.4

144�,72�

m�B � 180� � 120� � 60�

m�A � m�D � 90�

m�C � m�D � 180� � 41� � 139�

m�B � m�A � 41�

m�A � m�B � 180� � 67� � 113�

m�C � m�D � 67�

m�A � m�B � 180� � 80� � 100�

m�C � m�D � 80�

m�C � 180� � 128� � 52�

m�A � 180� � 71� � 109�

m�A � m�D � 180� � 115� � 65�

m�C � m�B � 115�

� 95 ft 2

��3.14��5.5� 2 � 26 cm2

Area � r 2 � 12�13��4�

r � 5.5 ft Area �12bh

� 9 cm2 � 12 m2

� 32 � 4 � 3

Area � s 2 Area � lw

� 1.618034

1 � �5

2�

1 � 2.2360682

�1 � �51 � �5 4 � 4

�1 � 5 � 4

1 � �5

2�

2�1 � �5

1 � �5

2�

2x

�1 � �5 � x

1 � �5 � 2 � x 5. Measurements will vary.

Drawing Conclusions:

1. cm 2. 35

3. Any two corresponding lengths or corresponding perime-ters have the same ratio; corresponding

4. The ratio of two corresponding areas is the square of theratio of corresponding lengths.

Lesson 8.3


1. No; the figures are only if the scale factor is 1.

2. No; the lengths of corresponding sides are not propor-

tional;

3. Yes; corresponding can be shown to be by theInterior Angles of a Quad. Thm., and lengths of corre-sponding sides are proportional

4.

5.

6.

7.


8.

9.

JKWX

�KLXY

�LMYZ

�JMWZ

�M � �Z;�J � �W, �K � �X, �L ��Y,

DEPQ

�EFQR

�DFPR

�D � �P, �E ��Q, �F � �R;

m�TUV � m�ABC � 180� � 70� � 110�

x � 10

3x � 30

53

�x6

159

�53

ABTU

�BCUV

�CDVW

�ADTW

�D � �W;�C � �V,�B � �U,�A � �T,

105

�147

�126

�84

�21

��

1510

�83

.

�

� are �.

�5�1.4� � 7

Measurement Photo 1 Photo 2 Ratio

AB 4.2 cm 3.0 cm

AF 7.8 cm 5.4 cm

CD 4.0 cm 2.8 cm

30 30 1

106 106 1

Perimeter of 24.8 cm 17.2 cmPhoto

24.817.2 � 1.4

��m�2

��m�1

42.8 � 1.4

7.85.4 � 1.4

4.23 � 1.4


Chapter 8 continued



10.

11. Yes; both figures are rectangles, so all 4 and

12. No; lengths of corresponding sides are not proportional;

13. No; and so corresponding arenot

14. No; and so corresponding are

not and so lengths of corresponding sides are not

proportional.

15. Yes; Sample answers:

16. No;

17. Yes; and

18. No; and so cor-

responding are not and so corresponding

sides are not proportional.

19. 20.

21.

22.

23. 24.

25.

26.

27.

28. 29. No; 1814

�188

�3018

1020

�12

3 � 3 � 2 � 2 � 10

m�G � m�C � 180� � 30� � 150�

x � 2

2x � 4

x4

�12

63

�21

5872.5

�45

� 58 PQRS: 16 � 10 � 12 � 20

� 72.5 JKLM: 25 � 15 � 12.5 � 20

y � 20 x � 12.5 w � 20

4y � 80 4x � 50 5w � 100

y

16�

54

x

10�

54

w25

�45

1512

�54

1215

�45

3014

�2010

,��

m�L � 180� � 118� � 62�,m�R � 65�

�XYZ~�CAB128

�96

�6.754.5

�32

;

�B � �Z�C � �X,�A � �Y,

63

�44

ABCD~FEHG

ABCD~EFGH,

65

�33

,�

�m�Q � 88�,m�K � 90�

�.�m�Q � 88�,m�B � 90�

75

�3.55

.

ABFG

�BCGH

�CDHE

�ADFE

�74

.

� are �

QRAB

�RSBC

�STCD

�TUDE

�QUAE

�T � �D, �U � �E;�Q � �A, �R � �B, �S � �C, 30. Yes; because A and B are parallelograms, the markedangles are to their opposite angles and the angles consecutive to the marked angles are supplements of themarked angles. So corresponding are . Also, becauseall 4 sides of A and all 4 sides of B are , the lengths ofcorresponding sides are proportional.

31. sometimes 32. sometimes 33. sometimes

34. sometimes 35. always 36. never

37. always 38. sometimes

39.

40.

41.

42.

43. Analog: Digital:

9x � 9�1.47� � 13.2 in.3x � 3�5.4� � 16.2 in.

16x � 16�1.47� � 23.5 in.4x � 4�5.4� � 21.6 in.

x � 1.47 x � 5.4

x2 � 2.1632 x2 � 29.16

337x2 � 729 25x2 � 729

256x2 � 81x2 � 729 16x2 � 9x2 � 729

�16x�2 � �9x�2 � 27 2 �4x�2 � �3x�2 � 27 2

y � 166 �152

� 712

y � 73 � 93 x �304

� 93� 4x � 30

�y � 73�� 360� � 116� � 61� � 90� x5

�64

x �82821

�2767

� 3937

21x � 828

y �48621

�1627

� 2317

21x � 126 � 702

21y � 486 21�x � 6� � 702

y

27�

1821

x � 6

39�

1821

x �19218

�323

� 1023

18x � 192

18x � 72 � 264

18�x � 4� � 264

Because y° is the supplementof 60°; y � 180 � 60 � 120.

x � 422

�1218

y � 9 x � 11

10y � 90 10x � 110

10y � 30 � 120 10x � 20 � 90

10�y � 3� � 120 10�x � 2� � 90

y � 3

8�

1510

x � 2

6�

1510

64

�32

��

�




Chapter 8 continued

44. No; the ratio of length to width for a standard screen

and for a digital screen. Then and

and

45. with a scale factor of The

perimeter of is The

ratio So,

46.

47.

48.

49. a. Figure 1:

b.

y �107

x

0 � b

6 � 6 � b

6 � �107 ��4.2� � b

y

x

1

1

y � mx � b

EA � 2.8

10�EA� � 28

EA4

�7

10

DE � 1.4 CD � 3.5

10�DE� � 14 10�CD� � 35

DE2

�710

CD5

�710

BC � 2.1 AB � 4.2

10�BC� � 21 10�AB� � 42

BC3

�7

10 AB6

�7

10

y � 6.4 cm x � 3 cm

5y � 32 5x � 15

51

�32y

51

�15x

9418.8

�51

so

x � 11.2 in.

5x � 56

25

�x

28

4:15

2:7.5

perimeter of ABCDperimeter of EFGH

�ABEF

.

perimeter of ABCDperimeter of EFGH

�2l � 2w

k�2l � 2w� �1k.

2�kl� � 2�kw� � k�2l � 2w�.EFGH

ABEF

�lkl

�1k.ABCD~EFGH

416

�39

.widthwidth

�39

,

lengthlength

�4

16169

�43

c. it is the reciprocal of the scale factor.

50. Sample sketch:

51. Since if you are standing at a point onEarth at the vertex of the triangles (E), it would appearthat the moon is completely blocking the sun’s light.

52.


53. 54.

55. 56.

57. 58.

59.

60.

61.

62.

64.

z � 120

5z � 600

5

24�

25z

x � 2

27x � 54

x9

�6

27

x � 9

9x � 81

9x � 99 � 180

3x� � 105� � �6x � 6�� 180�

x � 7

14x � 98

14x � 82 � 180

83� � 5x� � �9x � 1�� 180�

x � 49

x � 131 � 180

x� � 90� � 41� � 180�

�5 � 65 � ��1� � �

116

�2 � 52 � ��4� � �

76

10 � ��3�1 � ��2� �

133

5 � 42 � 9

� �17

�3 � ��7��6 � 0

�4

�6� �

23

8 � 43 � ��1� �

44

� 1

CD � 1120 miles

93,000,000�CD� � 103,800,000,000

93,000,000

240,000�

432,500CD

AECE

�ABCD

CDE~�ABE,�

moon

E D

B

AC

Earthsun

432,500 mi

240,000 mi

93,000,000 mi

m �107

;

63.

65.

b �3213

13b � 32

4

13�

b8

y � 38

2y � 76

4y

�2

19


Chapter 8 continued



66. 67.

Quiz 1 (p. 479)

1. 2.

3. 4.

5. 6.

7. 8.

Scale factor � 45:30 � 3:2

Ratio of perimeters �

Scale factor � 3:6 � 1:2

Ratio of perimeters �

9.

None are exactly similiar, but the and wallet sizes

are nearly similar .

10.

x � 318

in.

8x � 25

8

10�

2.5x

� 52.25

� 2.22, 7

3.25� 2.15�

5 7

85

�107

, 8

2.25�

103.25

, 5

2.25�

73.25

12

32

x � 3

18 � 6x

x � 30 24 � 6x � 6

x2 � 900 24 � 6�x � 1�

45x

�x

20 36

�x � 1

8

x � �70 � 8.37 x � �55 � 7.42

x2 � 70 x2 � 55

10x

�x7

5x

�x

11

x �9628

�247

�28x � �96

x � 21 4x � 32x � 96

x2 � 441 4x � 16�2x � 6�

7x

�x

63

42x � 6

�16x

d � 28 p � 10

5d � 140 3p � 30

57

�20d

p

15�

23

x � 21 x � 9

42 � 2x 2x � 18

18x � 42 � 20x 11x � 9x � 18

6�3x � 7� � 20x 11x � 9�x � 2�

3x � 7

5�

4x6

11

x � 2�

9x

Lesson 8.4

Activity (p. 480)

Sample answer:

The angles are both by the Triangle Sum Thm.;yes, the triangles are similar.


1.

2. Sample answer: any two points;

or

3. No; corresponding sides of s are not unless thescale factor of the s is Corresponding

4. No; corresponding .

5. Yes; all are so corresponding are

6.

7.

8. by the Reflexive Prop. of Congruence,

so by the AA Similarity Postulate.


9.

10.

11.

12. 13.

14. 15. 15; x15; y

LM; MN; NL�LMN

LMQP

�MNPN

�LNQN

�L and �Q, �M and �P, �LNM and �QNP;

VTST

�TWTU

�VWSU

�V and �S, �T and �T, �W and �U;

JKFG

�KLGH

�JL

FH

�J and �F, �K and �G, �L and �H;

�ABC~�BDC

�C � �C

MP � 10

40 � 4�MP�

84

�MP5

m�P � m�L � 53�

m�N � m�K � 90�;

m�J � m�M � 37�;

�.�60°�

� are not �

� are �.1:1.�

��~

5 � 10 � 4

�4

�4� �1

6 � 3�1 � 2

�3

�3� �1

ABXY

�64

�32

32 �

64 �

4.53 ;

80�

2

3

460�

40�

60�

40�

3 6

4.5

PN � 6

24 � 4�PN�

84

�PN3




Chapter 8 continued

16. 17.

18. No; and so corresponding are not

19. Yes; and so the s are

by AA Similarity Postulate;

20. No; so the lengths of corresponding sides are

not proportional.

21. Yes;

and so the s are by AASimilarity Postulate;

22. No; m ∠E � 94°, m ∠B � 94°, m ∠A � 54°, so corresponding are not

23. Yes; by Vertical Thm.,so the s are by AA

Similarity Postulate;

24. Yes; and so the s are by AA Similarity Postulate;

25. Yes; and so the s

are by AA Similarity Postulate;

26. Yes; and by the ReflexiveProp. so the s are by AA Similarity Postulate;

27. Sample answer:

28. Sample answer:

29. Slope of

so

�10, 0�

x � 10

�1��x� � 10

�12

�5 � 00 � x

↔BC �

0 � 36 � 0

� �12

�1 � ��2�2 � ��1� �

13

0 � ��1�

5 � 2�

13

�3 � ��1�

7 � 2� �

25

1 � 3

�3 � ��8� � �25

�PQR ~ �PST~�

�P � �P�PST � �TQR

�VWX ~ �VYZ.~�m�X � m�VZYm�W � m�VYZ

�ABC ~ �EDC.~�

m�B � m�D � 40�m�A � m�E � 50�

�JMN~�JLK.~�m�N � m�K � 50�

��NJM � �LJK

�.�

�XYZ ~ �GFH~��Z � �H �X � �G

m�Z � 55°

m�Z � 48° � 77° � 180°

2026

�1620

,

�PQR ~ �WPV

~��W � �RPQ �Q � �VPW

�.�

m�D � 47�m�C � 31�

x � 24 y � 16

15x � 360 15y � 240

18x

�1520

y

12�

2015

30. Slope of

so

31. Slope of

so

32. Slope of

so

33.

35.

37.

39.

41.

43.

x � 100

35° � 45° � x° � 180°

y � 27

24y � 648

24y � 72 � 576

24�y � 3� � 576

y � 3

32�

1824

p � 14

8p � 112

168

�p7

x � 20

6x � 120

6

15�

8x

615

�8x

CDE

�4 12, 0�

x � 412

2x � 9

�2��x� � 9

�2 �9 � 00 � x

↔BC �

0 � 84 � 0

� �2

�30, 0�

x � 30

�1��x� � 30

�15

�6 � 00 � x

↔BC �

0 � 15 � 0

� �15

�514, 0�

x � 514

4x � 21

�4��x� � 21

�43

�7 � 00 � x

↔BC �

0 � 43 � 0

��43

34.

36.

38.

40.

42.

z � 36

180 � 5z

45

�z

45

r � 26

11

11r � 28

114

�7r

y � 4

15y � 60

156

�10y

156

�10y

CD; CE; DE

mcrbg-0804-sk.qxd 5-25-2001 11:17 AM Page 167

Chapter 8 continued



44.

45.

46. 47.

48. Since and areright Since all right By theReflexive Prop. of Cong. so by the AA Similarity Post.

49. Since are both right they are by the Reflexive Prop. of Cong, soby AA Similarity Postulate

50. True; all right so the s are by AA SimilarityPostulate

51. False; all of any 2 equilateral s are so the s areby AA Similarity Postulate

52. True; since the vertex of each isosceles has measurethe measure of each base is

The s are by AA Similarity Postulate

53.

54. Answers will vary, but the slopes are always equal.

55. and so and are right

angles and so by Corresp.

Thm. So by AA Similarity Post.;

therefore so and

56. Sample answer: and thebuilding shadow

x � 31.25 ft

4x � 125

x5

�254

� 25 ftrod shadow � 4 ft,Rod � 5 ft,

PQ � 480 feet.PQ4

�7806.5

PQSR

�QRRT

�PQR ~ �SRT�

�PRQ � �TPR � ST�.

�SRT�QSR � QTPQ � QT

d � 1.5 m

2.4d � 3.6

2.43.6

�1d

2.46 � 2.4

�1d

~�

12�180� � 40�� 70�.�40�,

��

~��,��

~�� are �,

�ABE ~ �CDE�CED � �AEB

�.�,�ECD and �EAB

�JKL ~ �JMK�J � �J,�JMK � �JKL.� are �,�.

�JMK and �JKLJK � KL,KM � JL

z � 25 y � 80

450 � 18z 12y � 960

378 � 18z � 72 48y � 960 � 36y

378 � 18�z � 4� 48�y � 20� � 36y

14

z � 4�

1827

48y

�36

y � 20

x � 12

12x � 144

1218

�8x

s � 1312

4s � 54

49

�6s

57. a. and are right and andare by the Vertical Angles Thm., so

by AA Similarity Postulate

b.

d. Sample Answer: If point is added to the diagram so that and

then BCDE is a rectangle,and

58. Sample answer:

59. 60.


61.

62. 63.

64. is the midpoint of so

65.

66.

68.

70.

x � 69

1656 � 24x

2324

�x

72

x � 51

561 � 11x

17x

�1133

x �92

8x � 36

x

12�

38

MN �12�JL� �

12�24� � 12

MP �12�KL� �

12�32� � 16

KL � 32,KLN

KJ � 2�NP� � 2�23� � 46KJ

�1089 � 961 � �2050 � 5�82

��21 � 12�2 � �14 � ��17��2

h � 0.4 m

d � 25 m 10 � 25h

d

25 mm�

1 m1 mm

10 m

25 mm�

h1 mm

d25

�hr

AD � ��AE� 2 � �ED� 2 � �42 � 32 � �25 � 5.AE � AB � BE � 4,BE � CD � 3,

BE � CD,ED � BCm�E � 90�,

E

x �34

mi

4x � 3

3x � 3 � x

13

�x

3 � x

�ABX ~�DCX��DXC

�AXB��DCX�ABX

c.

AD � 5 mi

AX � DX � AD

DX � 3.75 mi

14.0625 � �DX� 2

32 � �2.25�2 � �DX� 2

AX � 1.25 mi

1.5625 � �AX� 2

12 � �0.75�2 � �AX� 2

67.

69.

71.

x � ±16

x2 � 256

8x

�x

32

x �3611

36 � 11x

102 � 11x � 66

102 � 11�x � 6�

3411

�x � 6

3

y � 8

12y � 96

3y

�1232




18. The ratios of the lengths of the given sides are the sameand the included are so the s are by SAS

Similarity Thm.

19. by Alt. Int. Thm. 20. by Alt. Int. Thm.

21. by Triangle Sum Thm.

22. 23.

24. 25.

26.

27. and included are So by

SAS Similarity Thm.

28. and so by

SAS Similarity Thm.

29.

30. Since and and

Then and, since

by SAS Similarity Thm.

B

Y

C ZA X

�ABC ~ �XYZ�B � �Y,BAYX

�BCYZ

YX � YZ.BA � BCYX � YZ,BA � BC

h � 140 ft

560 � 4h

5.6h

�4

100

r � 10

6r � 60

6

12�

5r

�EFG ~ �EJH�E � �E6

12�

48

p � 18

10p � 180

1015

�12p

�ABC ~ �BDC�.�1015

�8

12

�ABC and �EDC�BGC and �DFC,�AGC and �EFC,

x � 4�2 x � 21

48�2 � 12x 4x � 84

412

�x

12�2 4

12�

7x

x � 15 x � 12

3x � 45 3x � 36

39

�5x

39

�4x

82�

�45��53�

~��6:1�

Chapter 8 continued

Lesson 8.5


1.

2. AA Similarity Post.;

3. SAS Sim. Thm.;

4. are both

and

the s are by the SSS Similarity Thm.

5. all ratios are equal to so the s are

by SSS Similarity Thm.

6. and are � by the SSS Sim. Thm.

so the scale factor is

7. and are � by the SSS Sim. Thm.


8. and are by the SSS Sim. Thm.


9. Yes; so (or )

by SSS Similarity Thm.

10. Yes; SAS Similarity Thm.

11. No;

12. Yes; SAS Similarity Thm.

13. Yes; SSS or SAS

Similarity Thm.

14. Yes; by reflexive prop, and by Corresp. Post.; AA SimilarityPost.

15. SSS Similarity Thm.

16. If and then byTriangle Sum. Thm. Also, and so So s are by the AA Similarity Post.

17. The ratios of the lengths of corresponding sides are the

same, and the included are so the

s are by SAS Similarity Thm.~�

��186

�248

�31�,

~�m�E � 62�.m�F � 90�m�D � 28�

m�C � 90�m�B � 62�m�A � 28�

84

�168

�189

�21

;

�WXP ~ �WYZ;�

�XPW � �YZW�W � �W

�PQR ~ �DEF;1815

�3025

�2420

�65

;

68

�8

1023

�34

; �ABC ~ �LKJ;

3224

�2015

�1814

�PMS ~ �RMN;

�XZY�JKL ~ �XYZ3510

�3510

�288

�72

,

34

.1824

�2736

�3344

�34

,

~�TSU�XYZ

25

.820

�1025

�4

10�

25

,

�GHJ�DEF

32

.64

�4.53

�7.55

�32

,

�QRS�MNP

~

�16

212

�5

30�

636

�16

;

~�

ABMN

�BCNP

�ACMP

� 2;ABJK

�BCKL

�ACJL

�85

~ to �ABC,�JKL and �MNP

�ABC ~ �DFE

�ABC ~ �DEF

FHRX

�HGXS

�FGRS




Chapter 8 continued

31. Locate on so that and draw throughCorresp. and are as are corresp.

and so Then

But and so and

GH � DF. By the SAS Cong. Post.,Corresp. and are so by theTransitive Prop. of Cong. by AASimilarity Postulate.

32.

33.

34.

35. Julia and the flagpole are both perpendicular to theground and the two s formed have a shared angle. Then the s are by the AA Similarity Postulate

36.

so perimeter of

The length of is

B

37.

A

XZ � YZ � 70 � 50 � 120

YZ � 50

2�YZ� � 100

25

�20YZ

XY � BC � 105 � 20 � 125;

XY � 105

2�XY� � 210

42XY

�25

XY

�ABC � 28 � 20 � 42 � 80;

AC � 28;

5�AC� � 140

AC70

�25

~�

�

x � 25 ft

7x � 175

7

35�

5x

x � 18 ft

80x � 1440

x

48�

3080

x � 80 m

2000 � 25x

2500 � 25x � 500

2500 � 25�x � 20�

20

x � 20�

25125

�ABC ~ �DEF�F � �C�,BHG� F

�BGH � �EDF.

ACGH

�ACDF

GB � DE,ABDE

�ACDF

ABGB

�ACGH

.�ABC ~ �GBH.BHG,� C

�,BGH� AG � to AC.GHGB � DEABG 38. Assume that the posts and are perpendicular to

the ground, . Then and are all toso they are all to each other. Then ∠ADC, ∠BCD,

∠EFD, and ∠EFC are all right and so are all �. ∠DAC � ∠FEC and ∠DBC � ∠DEF by the Corr.

Post. So ADC EFC and BCD EFD by the

AA Similarity Post. Then and by

the definition of similar triangles. Then add equals to

equals and solve for EF as follows:

Addition Prop. of Equality

Combine fractions.

Simplify.

Simplify.

Combine fractions.

Simplify.

Multiply.

Divide and simplify.

The length of is ft.1717

EF

EF �1207

� 1717

7 � EF � 120

7 � EF120

� 1

3 � EF � 4 � EF120

� 1

EF40

�EF30

� 1

EF40

�EF30

�DCDC

EF40

�EF30

�FC � DF

DC

EF40

�EF30

�FCDC

�DFDC

EF30

�DFDC

EF40

�FCDC

�~��~��

�

�DC�EFAD, BC,DC

BCAD




Chapter 8 continued


39.

40.

41.

42. 43. 44. 45.

46. A reflection in the x-axis changes the sign of they-coordinate;

47. A reflection in the y-axis changes the sign of the x-coordinate;

48. A reflection in the y-axis changes the sign of the x-coordinate;

49. A reflection in the x-axis changes the sign of the y-coordinate;

Quiz 2 (p. 496)

1. Yes;

by Alt. Int. Thm.;

by Vert. Thm.;

by Alt. Int Thm.

2. Yes;

by Corresp. Post.

by Corresp. Post.

3. No;

so and socorresp. are not

4. No; 5. Yes;

6. Yes;

7.

Math & History (p. 496)

Sample answer:

M

1 in.

1 in.58

x � 10 mi

7x � 70

5x

�7

14

31

�62

�7

�73�

36

�6

12�

714

43

�76

�87

�.�

m�P � 94�m�A � 43�m�J � m�H � 42�;

180� � 96� � m�J � m�H � 84�;

m�V � 32°

m�V � 47° � 101° � 180°

�m�VSU � 47�

�m�U � 101�

m�P � 47�;

m�P � 101� � 32� � 180�

�m�A � 53�

�m�ANB � 46�

�m�B � 81�

m�E � 81�;

m�E � 53� � 46� � 180°

��5, 1�

�3, �10�

�2, 7�

�0, �5�

�5�7�10�12

m�ABC � 128�m�ABD � m�DBC � 64�;

m�ABD � m�DBC �12�m�ABC� �

12�36°� � 18�

m�ABD � m�DBC �12�m�ABC� �

12�77°� � 38.5�

Technology Activity

Sample answers:

Investiagte

1. Measurements will vary, but

2. The ratios will remain the same.


Make a Conjecture

4. When a line to one side of a intersects the other twosides, it divides them proportionally.

Investiagte

5. Measurements will vary, but

Make a Conjecture


7. The bisector of an of a divides the opp. side into 2 segments whose lengths are in the same ratio as thelengths of the other 2 sides of the .

Extension

The s are if and only if the original is isosceles. (If so, the resulting s are not only , they are �.)

Lesson 8.6

Activity (p. 500)

Sample answer:

1–3.

4. The lines divide the transversals proportionally.

Since then

and


1. parallel; Proportionality Converse

2.

3. True by Proportionality Thm.

4. True by Corresp. Post., AA Similarity Post.,and def. of s .

5. True by Corresp. Post., AA Similarity Post.,and def. of s .�~

�

�~�

�

BRRC

�ABAC

�

AJ � JK � KL � LB.

AJJK

�JKKL

�KLLB

� 1ADDE

�DEEF

�EFFG

� 1,

�

A B

C

DE

FG

~�

�~�

�

��

BRBQ

�RPQP

.

��

BDDA

�BEEC

.

or about

1:1.618

1:1.625

1:158




Chapter 8 continued

6. False; statement does not follow from similarity.

7. 8. 9. 10.


11. Yes; 12. Yes;

13. No; 14. Yes;

15. Yes; Proportionality Converse

16. No; only one angle is given (∠N is � to itself), which isnot enough to prove that

17. Yes; Corresp. Converse

18. Yes; Corresp. Converse

19. No; and are sides of and is aside of , but is not a side of a , so this isnot a proportion of lengths of corresponding sides. Theproportion does not give enough information to prove

s or conclude that

20. Yes; def. of s and Corresp. Converse.

21.

23.

25.

27.

f � 29.4

15f � 441

f

21�

2115

p � 14

12p � 168

7p

�1224

x � 6

20x � 120

8

20�

x15

a � 3

15a � 45

9a

�155

��~

LP � MQ.�~

�LM�LNPLP�MNQMQMN

�

�

LP � MO.

�

129

�2015

3415

�3516

12.55

�104

164

�82

EAGEADCE29.

m;

30. Lot since it has the longest distance of ocean frontage.

31. Statements Reasons

32. Draw intersecting at (Through any 2 pointsthere is exactly 1 line.) By the Proportionality Thm.,

since and and

Then by the Transitive property of equality.

33. Draw a line to through and extend to intersect the line at ( is not to because it

would also have to be to .) Then Also,

corresp. and are as are alt. int. and Since by theTransitive prop. of cong. By the Converse of the BaseAngles Thm., or Then by the

Substit. prop. of equality,YWWZ

�XYXZ

.

XA � XZ.XA � XZ

�A � �AZX�YXW � �WXZ,AZX.� WXZ�,A� YXW

YWWZ

�XYXA

.XW�

AZ�XYA.�XY� � Post.�ZXW �

CBBA

�DEEF

DXXA

�DEEF

.CBBA

�DXXA

k2 � k3,k1 � k2

�

X.BEAD

A

Lot C 34.0 m

97�Lot C� � 3294

2797

�Lot C122

Lot B 40.2

3904 � 97�Lot B�

3297

�Lot B122

Lot A 47.8 m;

97�Lot A� � 4636

3897

�Lot A122

22.

24.

26.

28.

q � 12

210 � 17.5q

17.5

1.25q�

1412

q � 27.5

21q � 577.5

21

17.5�

33q

z � 15

300 � 20z

300 � 12z � 8z

12�25 � z� � 8z

25 � z

z�

812

c � 9

288 � 32c

288 � 12c � 20c

12�24 � c� � 20c

24 � c

c�

2012

1.

2.

3.

4.

5.

6.

7.

8.DABD

�ECBE

1 �DABD

� 1 �ECBE

BDBD

�DABD

�BEBE

�ECBE

BD � DABD

�BE � EC

BE

BABD

�BCBE

�DBE ~ �ABC

�DEB � �ACB�EDB � �CAB;

DE � AC 1. Given

2. Corresp Post.

3. AA Similarity Post.

4. Def. of s

5. Segment Addition Post.

6. Addition of fractions

7. Substit. Prop. of Equality

8. Subtraction Prop. of Equality

�~

�




Chapter 8 continued

34.

35.

36.

37.

38. In the diagram for Ex. 31 on page 504, suppose that

Then

So, by

the Segment Addition Post. and the substitution prop.of equality. Since by the Reflexive Prop of Cong., by the SAS Similarity Thm.Then corresp. and A are and bythe Corresponding Angles Converse.

DE � AC �� BDE�ABC ~ �DBE

�B � �B

BABD

�BCBE�If

ab

�cd

, then a � b

b�

c � dd �.

DA � BDBD

�EC � BE

BE.

DABD

�ECBE

.

x 1040 ft

2800x 2,912,000

1120

x

28002600

x 1400 ft

2600x 3,640,000

x

1300

28002600

UR � 21

44�UR� � 924

UR14

�6644

PR � 27 SN � 8

18�PR� � 486 39�SN� � 312

PR18

�2718

SN12

�2639

LN � 8 MT � 8.4

27�LN� � 216 18�MT� � 151.2

LN18

�1227

MT5.6

�2718

HJ � 15.8 FG � 13.8

21.6�HJ� � 341.28 21.6�FG� � 298.08

HJ

31.6�

10.821.6

FG27.6

�10.821.6

BC � 4 GJ � 4

21.6�BC� � 86.4 11.9�GJ� � 47.6

BC10.8

�8

21.6 GJ

13.6�

3.511.9

DF � 5.25 AB � 7

13.6�AB� � 71.4 13.6�AB� � 95.2

DF11.9

�6

13.6

AB11.9

�8

13.6 39. a.

c.

d. Sample answer: If lines are cut by a transversal,corresp. are so and then by AA Similarity Post.

40. Sample construction:

so


41.

42.

43.

44.

45.

46.

47. Sample answer:

48. Sample answer:

D � 20

400 � D 2

162 � 122 � D 2

2

2

y

x

D

h � 15

h � �225

225 � h 2

122 � 92 � h 2

2

h

2

y

x

� �92 � ��8�2 � �145��4 � ��5��2 � �0 � 8�2

� �17 2 � 4 2 � �305��7 � ��10��2 � �4 � 0�2

� ��9�2 � ��5�2 � �106��2 � 11�2 � ��5 � 0�2

� �72 � 72 � �98 � 7�2��2 � ��9��2 � �6 � ��1��2

� �72 � ��16�2 � �305��4 � ��3��2 � ��9 � 7�2

� �92 � 162 � �337��5 � ��4��2 � �10 � ��6��2

xy

�zp

B

E

C

Dx

z

p

y A

�ABC ~ �DBE�BED � �C,�BDE � �A�,�

2 �

CE � 12

10�CE� � 120

610

�CE20

BE � 15

8�BE� � 120

68

�BE20

b. Sample answers:

BABD

�ACDE

BDBA

�BEBC

, BDDA

�BEEC

,




Chapter 8 continued

49. Sample answer:

50. Sample answer:

51. reflection 52. glide reflection 53. rotation

Lesson 8.7


1. similar

2. She found , rather than

3. Enlargement; the scale factor is which is

4. similar

5. larger; enlargement

6.

7. yes; Sample answer: A preimage and its image after adilation are


8. Reduction; the dilation has center and a scale factor of

9. Enlargement; the dilation has center and scale factor of

10. Enlargement; the dilation has center and scale factor of

y � 16 x � 8

2y � 32 2x � 16

21

�32y

21

�16x

2814 �

21.

C

249 �

83.

C

614 �

37.

C

~.

y

x

1

1A

A� D�

D

B C

C�B�

�since k > 1�

> 1.42

�21

� 2

CP�

CP.

CPCP�

� � 10

100 � �2

82 � 62 � �2

2

2

y

x

ll

h � 6�2

72 � h2

62 � 62 � h2

1

1

y

x

h

11. Reduction; the dilation has center and a scale factor of

12.

13.

14.

15.

16. same as the scale factor

17.

18.

19.

20. 65:39

5:3

21. 30:22.5

4:3

y � 6.3 x � 7.2

12y � 75.6 12x � 86.4

y

8.4�

912

x

9.6�

912

;

t � 1820 � r

15t � 270180 � 9r

159

�30t

; 159

�r

12;

D

F E

D �

F �E �

HD

F E

D �

F � E �

F E

D

D �

F � E �

G

2; G; 2:1;

V��3, �1� → V� � 4��3, �1� � ��12, �4�

U��1, 1� → U� � 4��1, 1� � ��4, 4�

T��3, 4� → T� � 4��3, 4� � ��12, 16�

S��5, 2� → S� � 4��5, 2� � ��20, 8�

G��3, �4� → G� �13��3, �4� � ��1, �4

3�F�5, �3� → F� �

13�5, �3� � �5

3, �1�E�3, 2� → E� �

13�3, 2� � �1, 23�

D��5, 4� → D� �13��5, 4� � ��5

3, 43�R�1, 1� → R� � 2�1, 1� � �2, 2�

Q�4, 0� → Q� � 2�4, 0� � �8, 0�

P�3, 5� → P� � 2�3, 5� � �6, 10�

M��5, �3� → M� �12��5, �3� � ��21

2, �112�

L�2, �3� → L� �12�2, �3� � �1, �11

2�K�2, 3� → K� �

12�2, 3� � �1, 11

2�J��5, 3� → J� �

12��5, 3� � ��21

2, 112�

z � 25y � 20; x � 20;

2x � 40

25

�8x

1025 �

25.

C




Chapter 8 continued

22. Sample answer:

reduction;

23.

enlargement;

24.

25.

27.

29.

31.

x � 1.7 in.

10x � 17

210

�x

8.5

x � 4.8 in.

1.2x � 5.76

1.27.2

�0.8x

7:1

D 9.2 cm

2.7D � 24.9

2.78.3

�3D

bulb preimage imagecircle

oflight

AC � 9

B�C� � 28 4�AC� � 36

41

�B�C�

7 41

�36AC

;

k �205

�41

;

B�

C �

A�

A

C

B

9 7

5

20

2836

A�C� � 4 B�C� � 3

13

�A�C�

12 13

�B�C�

9;k �

26

�13

;

B�

C �A�

A C

B

6

23

4

12

9

32. The s are All 3 s are to so all the corresp. The scale factor of each dilation is 2,so each side of every image is twice as long as the corresp. side of Then the corresp. sides of the 3 s are and the 3 s are by the def. of s .

33. Sample answer:

I would show the student this figure and explain that Lrepresents the light source, CP the height of the puppet,and SH the height of the image. I would tell the studentthat a dilation transforms a figure in such a way that theoriginal figure (or preimage) and the figure after the dilation (the image) are similar. In the figure, the centerof the dilation is L and the scale factor is the ratio of LSto LC.

H

S

C

P

L

��

�PQR.�

� are �.�PQR,~��.�

26.

28.

30.

x 2.33 cm

12x � 28

x14

�2

12

x � 8.75 in.

1.25x

�17

I 6.1 cm

2.7I � 16.6

2.78.3

�2I


Chapter 8 continued



34. Sample answer:

35. since this is a reduction. C

36. or D

37. Sample answer: Let have sides 4, 6, 8 and letThen would have sides of 2, 3, 4. The

second dilation would make twice as large so

would have sides 4, 6, and 8. Therefore thenew image is the original figure.


38. 39.

40. 41.

42.

44. Yes; Sample answer: and by theAlt. Int Thm; so the s are by AA Similarity Post.

Quiz 3 (p. 513)

1. 2. 3. 4.

5. Enlargement; the dilation has center and scale factor

6. Reduction; the dilation has center and scale factor

7. reduction; larger

8. k �188

�94

k �21

21 � 42�

2163

�13

.

C

k �5 � 5

5�

105

� 2.

C

FAAFCEBD

~��

�R � �S�P � �T

x � 22

x2 � 484

11x

�x

44

a � 7 a � 11

a2 � 49 a2 � 121

a2 � 1 � 50 a2 � 4 � 125

a2 � 12 � ��50�2 a2 � 22 � �5�5�2

b � 14 c � 13

b2 � 196 169 � c 2

64 � b2 � 260 25 � 144 � c 2

82 � b2 � �2�65�2 52 � 122 � c 2

�A�B�C�

�A�B�C�

�A�B�C�k � 2.�ABC

3313%2

6 � 0.3313

k < 1k �26 �

13;

Technology Activity (p. 514)

Investigate

1. the ratio is the reciprocal of the scale factor of the

dilation.

2. the ratio is the reciprocal of the scale factor of the

dilation.

3. no 4. . 5.

Conjecture

6. If the scale factor of a dilation is a:b, then the ratio of thearea of a polygon to the area of its image after a dilationis

Extension

7. Sample answer: Let be a side of a polygon,

its image after the first dilation, and its imageafter the second. Since the first image is to the pre-image and the second is to the first, the transitive properties of and equality can be used to show the

second image is to the pre-image. Then so

Also Therefore, the scale factor of the dilation that maps theoriginal polygon to the final one is yx.

Chapter 8 Review (pp. 516–518)

1.

3.

5.

7.

8.

x � 45

3x � 135

53

�x

27

m�F � 67� � 180�

m�F � 113�

3018

�53

x � 39 in.

13

�13x

x � 4

�2x � �8

2x � 12 � 4x � 4

2�x � 6� � 4�x � 1�

2x � 1

�4

x � 6

x �212

21 � 2x

3x

�27

A�B� � y � A�B� � y � x � AB.A�B� � x � AB.

ABA�B�

�1x

~

�~

~A�B�A�B�

ABxy or yx.

a 2:b 2.

41

A�B�C�D�E� is inside ABCDE

21

;

21

;

43. Yes; Sample answer:

and

so the s are by the SAS

Similarity Thm.

~�

CALJ

�CBLK

�C � �L

2.

4.

6.

4000 oz� 1 lb16oz� � 250 lb

x � 4000 oz

3x � 12,000

31000

�12x

d � 7

4d � 28

7d � 28 � 3d

7�d � 4� � 3d

d � 4d

�37

a � 9

9a � 9 � 10a

9�a � 1� � 10a

a � 15

�2a9

mcrbg-080R-sk.qxd 5-25-2001 11:17 AM Page 176



Chapter 8 continued

9.

10. Yes; so and the s by the AA Similarity

Post;

11. No; andtherefore corresp.

are not

12. Yes; vertical are and so are andThe s by the AA Similarity Post.;

13. No;

14. Yes; and vertical are , so the s are by theSAS Similarity Thm.

15. 16.

17.

Chapter 8 Test (p. 519)

1. 2.

3. 4. 2

5. 36.

7. 8. No;

9. since all right are Since by the Reflexive prop. of cong.,

by the AA Similarity Post.

10.1525

�35

�RSQ ~�RQT �R � �R

�.��RSQ � �RQT

FG � 4.8

2.8�FG� � 13.44

1.52.25

1.44.2

2.83.2

�4.2FG

EF � 1.6

2.8�EF� � 4.48

2.83.2

�1.4EF

3 � y

z � 1

110z � 110

11110

�z

10

y � 24 x � 4

15y � 360 9x � 36

18y

�1520

x3

�129

h � 161659

59h � 960

35h � 960 � 24h

35h � 24�40 � h�

3524

�40 � h

h

y � 10.5 x � 22

10y � 105 12x � 264

15y

�107

1224

�11x

~��2520 �

37.530

2114 �

3926

4227

�PQN ~ �SRQ.are ~�R.

� N�� PQN and SRQ

�.�

m �J � 180� � �64� � 75�� 41�;m �G � 180� � �38� � 75�� 67�

�STU ~ �VWXare ~��S � �V

m�S � 180� � �104� � 48�� 28�,

HJKLDEFG

�2�18� � 2�27�2�45� � 2�30� �

90150

�35

11. Yes; Sample answer: Since is a right isalso a right Also, since corresp.

are Then by the AASimilarity Post.

12.

13. Yes; Proportionality Converse

14. Yes; Corresponding Converse

15. Yes; Sample answer: by SAS SimilarityThm., def. of s , and Corres. Converse.

16.

17. No;

18.

Chapter 8 Standardized Test (pp. 520–521)

1. B 2.

3.

C

5. ;

E

6. B; and are not corresponding sides.

7. 12 to 4

3 to 1

A

TUPR

y �152

12y � 90

12y � 36 � 126

12�y � 3� � 126 x � 106

1218

�7

y � 3 x� � 74� � 180�

7x � 7�3� � 21

2x � 2�3� � 6

x � 3

18x � 54

2�9x� � 54

2�2x � 7x� � 54

20 ft5 yd

�20 ft15 ft

�43

D

k �9 in.3 ft

�9 in.36 in.

�14

78

1418

R�T� � 5 S�T� � 3

4�R�T�� 20 4�S�T�� 12

14

�R�T�

2014

�S�T�

12k �

624

�14

��~�LHM ~ �JHK

�

�

x � 12

5x � 60

35

�x

20

�RSQ ~�QST�.� RQS and T�RSQ ~ �RQT,�.

�QST�,�RSQ

18. Reduction;

b � 17.5

4b � 70

47

�10b

k �2442

�47

;

4.

B

x � 64

x2 � 4096

16x

�x

256


Chapter 8 continued



8.

;

E

9.

B

11. the dilation is a reduction, so theperimeter of the pre-image is greater.

A

12.

C

13. 14. 15.

16.

17. The colors are given in percents, which stay the sameregardless of the number of cars manufactured.

18. a. 7.5

b.

c.

d.

19.187.5

�3615

�125

m �DGF � m �DCB � 84�

EF � 12.5

18�EF� � 225

EF30

�7.518

BC � 33.6

7.5�BC� � 252

7.518

�14BC

800 0.13 � 104 cars

12,560 0.05 � 628 cars39

�13

820

�25

k �A�B�

AB�

13

AB � 3; A�� 1;

x �5416

�278

16x � 54

163

�18x

so AB � 35, BC � 30and perimeter � 105

AC � 40

7�AC� � 280

78

�35AC

20.

21.98.441

�125

� 41

perimeter of EFGD � 14 � 7 � 7.5 � 12.5

� 98.4

perimeter of ABCD � 30 � 33.6 � 16.8 � 18

DC � 16.8

7.5�DC� � 126

7DC

�7.518

10.

C

CD � 20

15�CD� � 300

2515

�CD12




Chapter 8 continued

Algebra Review (pp. 522–523)

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

� 5�7

� 2�7 � 3�7

�28 � �63 � �4 � �7 � �9 � �7

� �16�3

� �7�3 � 9�3

��147 � �243 � ��49 � �3 � �81 � �3

� 21�2

� 11�2 � 10�2

�242 � �200 � �121 � �2 � �100 � �2

� �5

� 5�5 � 4�5

�125 � �80 � �25 � �5 � �16 � �5

� 4�11

� 2�11 � 2�11

�44 � 2�11 � �4 � �11 � 2�11

�64 � �28 � 8 � �7 � �4 � 8 � 2�7

� 2�2

� 5�2 � 3�2

�50 � �18 � �25 � �2 � �9 � �2

�75 � �3 � �25 � �3 � �3 � 5�3 � �3 � 6�3

�225 � 15

�320 � �64 � �5 � 8�5

�288 � �144 � �2 � 12�2

�243 � �81 � �3 � 9�3

�50 � �25 � �2 � 5�2

�80 � �16 � �5 � 4�5

�27 � �9 � �3 � 3�3

�40 � �4 � �10 � 2�10

�72 � �36 � �2 � 6�2

�45 � �9 � �5 � 3�5

�52 � �4 � �13 � 2�13

�121 � 11

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.2�3�6

�2�3 � �6�6 � �6

�2�18

6�

�9 � �23

�3�2

3� �2

5�7

�5�7

�7 � �7�

5�77

4�3

�4�3

�3 � �3�

4�33

�10�11�2� 102�112 � 100 � 11 � 1100

�5�5�2� 52�52 � 25 � 5 � 125

�2�3�2� 22�32 � 4 � 3 � 12

�8�3�2 � 82�32 � 64 � 3 � 192

�4�2�2� 42�22 � 16 � 2 � 32

�6�5�2� 62�52 � 36 � 5 � 180

�5�4��2�4� � 10 � 4 � 40

� 112

� 56 � 2

� �7�2��8�2� ��98��128� � ��49 � �2��64 � �2��32��2� � �64 � 8

��21��24� � �504 � �36 � �14 � 6�14

� 18 � 2 � 36

� �3�2��6�2� ��18��72� � ��9 � �2��36 � �2��6�2��2�2� � 12 � 2 � 24

� 330

� 110 � 3

� �11�3��10�3�� 363��300� � ��121 � �3��100 � �3�

� 21�10

� 3 � 7 � �10

� 3 � �49 � �10

�3�14��35� � 3�490

��13��26� � �338 � �169 � �2 � 13�2

� 4�5

� 2�5 � 3�5 � �5

�20 � �45 � �5 � �4 � �5 � �9 � �5 � �5


Chapter 8 continued



40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

52.

53.

55.

57.

59.

61.

x � ±7

x2 � 49

6x2 � 294

x � ±6

x2 � 36

7x2 � 252

x � ±4

x2 � 16

x2 � 4 � 12

x � ±17

x2 � 289

x � ±3

x2 � 9

�50�75

��50 � �75�75 � �75

��3750

75�

�625 � �675

�25�6

75�

�63

�27�45

��27 � �45�45 � �45

��1215

45�

�81 � �1545

�9�15

45�

�155

�32�5

��32 � �5�5 � �5

��160

5�

�16 � �105

�4�10

5

�18�10

��18 � �10�10 � �10

��180

10�

�36 � �510

�6�510

�3�5

5

�12�24

��12 � �24�24 � �24

��12 � �12 � �2

24�

12�224

��22

9�52

�9�52

�52 � �52�

9�4 � �1352

�18�13

52�

9�1326

3�5�20

�3�5 � �20�20 � �20

�3�100

20�

3020

�32

4�12

�4�12

�12 � �12�

4�1212

��4 � �3

3�

2�33

�5�10

��5 � �10�10 � �10

��5010

��25 � �2

10�

5�210

��22

16�24

�16�24

�24 � �24�

16�2424

�2�4 � �6

3�

2 � 2 � �63

�4�6

3

4�8

�4�8

�8 � �8�

4�88

��82

��4 � �2

2�

2�22

� �2

�183�2

��18 � �23�2 � �2

��363 � 2

�66

� 1

2�3�5

�2�3 � �5�5 � �5

�2�15

5

54.

56.

58.

60.

62.

x � ±�10

x2 � 10

4x2 � 40

4x2 � 5 � 45

x � ±8

x2 � 64

3x2 � 192

x � ±�13

x2 � 13

x2 � 7 � 6

x � ±�10

x2 � 10

x2 � 3 � 13

x � ±25

x2 � 625




Chapter 8 continued

63.

65.

67.

69.

71.

73.

x � ±13

169 � x2

25 � 144 � x2

52 � 122 � x2

x � ±4

x2 � 16

x2 � 9 � 25

x2 � 32 � 5 2

x � ±�6

x2 � 6

8x2 � 48

8x2 � 12 � 36

x � ±1

x2 � 1

10x2 � 10

10x2 � 16 � �6

x � ±2

x2 � 4

11x2 � 44

11x2 � 4 � 48

x � ±3

x2 � 9

2x2 � 18

2x2 � 5 � 23 64.

66.

68.

70.

72.

x � ±24

x2 � 576

49 � x2 � 625

7 2 � x2 � 25 2

x � ±5

x2 � 25

5x2 � 125

5x2 � 61 � 64

x � ±�7

x2 � 7

5x2 � 35

5x2 � 6 � 29

x � ±�2

x2 � 2

6x2 � 12

6x2 � 3 � 9

x � ±�5

x2 � 5

9x2 � 45

9x2 � 7 � 52


Documents

CHAPTER 8mrjaffe.net/GeomRef/unit8solutions.pdf · Chapter 8continued 8.1 Mixed Review (p. 464) 68. 69. 70. 71. 72. 73. and 74. and 75. and 76. Lesson 8.2 8.2 Guided Practice (p