chapter chapter test a 6 for use after chapter 6 · 2013-08-11 · a similarity statement and the...

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GeometryChapter 6 Assessment Book110

Simplify the ratio.

1. 34 cm

} 4 cm

2. 10 ft

} 30 in.

3. 4 lb

} 8 oz

4. 2 L

} 50 mL

Solve the proportion.

5. 3 }

8 5

9 }

x 6.

x }

30 5

7 }

15 7.

5 }

10 5

x 1 1 }

4 8.

2 }

3x 2 10 5

8 }

20

Find the geometric mean of the two numbers.

9. 6 and 24 10. 16 and 25 11. 12 and 30

Use the diagram and the given information to fi nd the unknown length.

12. Given BD

} DA

5 BE

} EC

, fi nd BE. 13. Given JM

} PS

5 ML

} SR

, fi nd PS.

B

CA

ED8

20

6

J K

M L P

S R

28

21

24

Determine whether the polygons are similar. If they are, write a similarity statement and fi nd the scale factor.

14. J K

M L

P

S R25

25

1515

66

10

10

15.

16

28

16.5 12

21

T V

Y

Z X

U

22

In Exercises 16–19, determine whether the triangles are similar. If they are, write a similarity statement.

16. 408

508

B

C

G

H FA

17.

428

958

468

NJ

M

K

L

Answers

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

CHAPTER

6 Chapter Test AFor use after Chapter 6

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GeometryChapter 6 Assessment Book 111

CHAPTER

6

Answers

18.

19.

20.

21.

22.

23.

24.

25.

26.

18.

P RU W

V

12

1216

8

8

4

19.

G

D

H E

F

10

15

24

36

Find the value of x.

20.

x

9

15

20

21.

x9

6 16

22.

x

50

35

40

23.

x

19.5 18

24

24. A photographer is enlarging an original photo that measures 5 inches by 5 inches. The enlargement is 15 inches by 15 inches. What is the scale factor of the enlargement?

25. An architect is making a drawing of a house to scale. The door of the house is 70 inches tall by 30 inches wide. The drawing of the door is 7 inches tall by 3 inches wide. What is the scale factor of the reduction?

26. The perimeter of a rectangular corn fi eld is 440 meters. The ratio of its length to its width is 7 : 4. What are the length and width of the fi eld?

Chapter Test A continuedFor use after Chapter 6


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Answers

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

Chapter Test BFor use after Chapter 6

Simplify the ratio.

1. $25 : $5 2. 40 cm

} 2 cm

3. 1 mi

} 10 ft

4. 9 ft

} 12 in.

5. 3 L : 100 mL 6. 3 gallons

} 4 quarts

In the diagram, n ABC , nXYZ.

7. Find YZ. 34

A C

B

6

7.5X Z

Y

8. Find AC.

In the diagram, ABCDE , FGHJK.

9. Find the value of x. 4

xA C

E

B

D

10

10

12

8

8

J H

FK

G 10. Find the perimeter of ABCDE.

Determine whether the triangles are similar. If so, write a similarity statement and the postulate or theorem that justifi es your answer.

11.

35°A DE

CB 12.

35

6L

M

N

4

7

6

R

S

Determine the value of x that makes n ABC , nXYZ.

13.

14

810

A

C

B 14.

4

3C B

A X

Y Z

8

6(x 2 5)°

Y

X

Z

1417.5

x 1 2

CHAPTER

6


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Answers

15.

16.

17.

18.

19.

20.

21.

Chapter Test B continuedFor use after Chapter 6

In Exercises 15 and 16, fi nd the length of } AB .

15.

86

2

A

C

B D

E 16.

15

25

A BC

20

E

D

17. A photographer is enlarging an original photo that measures 8 inches by 10 inches. The enlargement is 16 inches by 20 inches. What is the scale factor of the enlargement?

18. An architect is making a drawing of a house to scale. The door of the house is 72 inches tall by 36 inches wide. The drawing of the door is 6 inches tall by 3 inches wide. What is the scale factor of the reduction?

19. The perimeter of a rectangle is 24 inches. The ratio of the length to the width is 2 : 1. Find the length and the width.

20. The perimeter of a rectangle is 65 inches. The ratio of the length to the width is 4 : 1. Find the length and the width.

21. You are making a scale model of your neighborhood. The distance between two consecutive parallel streets is 200 feet. You use a scale

factor of 1 }

80 to build your model. What is the distance between

Catabay Street and Skelly Street on your model? Catabay Street

Market Street

Skelly Street

CHAPTER

6

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Answers

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

Chapter Test CFor use after Chapter 6

Simplify the ratio.

1. 3 gallons

} 27 quarts

2. 500 mm

} 2.5 m

3. 150 lb

} 100 oz

Solve the proportion.

4. 6 }

13 5

3x }

91 5.

x 1 6 }

x 5

5 }

4 6. 3 }

10 5

5x 1 1 }

18x 2 6

Use the diagram and the given information to fi nd the unknown length.

7. Given BC

} CF

5 AD

} DE , fi nd AE. 8. Given PR

} PS

5 RQ

} ST

, fi nd ST.

A B

FE

D C

13

53

R

T

P

S

32

2621

10

9. The lengths of the legs of right triangle FGH are 12 meters and 16 meters. The shortest side of nJKL is 2.4 meters and nJKL , nFGH. How long is the hypotenuse of nJKL?

In the diagram, nLMN , nPQR.

10. Find the scale factor M

L N

P R

117

1735

1212

of nPQR to nLMN.

11. Find the length of thealtitude shown in nPQR.

12. Estimate the lengths ofLM and PQ. Round youranswers to the nearest tenth.

13. Find the 10th, 11th, 12th, and 13th terms of the Fibonacci sequence.

14. Find the ratios of the consecutive terms from Exercise 13.

CHAPTER

6


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Answers

15.

16.

17.

18.

19.

20.

21.

22.

23.

Chapter Test C continuedFor use after Chapter 6

See left.

In Exercises 15–18, determine whether the triangles are similar. If they are, write a similarity statement.

15. B

CD

EA 12

6

8

4x

2x

16

16.

P R

Q

S

U T

17.

N M

KL

J 18. E

D H

G

F

Find the value of x.

19.

12

9

x 2 4

x

20.16

18

36

3x 1 11

Draw a dilation of the polygon with the given vertices using the given scale factor k.

21. A(212, 26), B(26, 23), 22. A(0, 0), B(0, 2), C(2, 2), D(4, 0);

C(23, 6), D(212, 6); k 5 1 }

6 k 5 2.25

x

y

1

1

x

y

1

1

23. You take 450 U.S. dollars to the bank to exchange for European euros. The exchange rate on that day is about 0.82 euros per U.S. dollar. How many European euros did you get for the 450 U.S. dollars?

CHAPTER

6

See left.


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A10GeometryAssessment Book

Standardized Test C

1. C 2. D 3. C 4. A 5. C 6. B 7. B 8. A

9. D 10. B 11. A 12. B 13. 28.45

14. 7.9 , x , 55.1

15. a. By the Pythagorean Theorem, the distance

is Ï}

452 1 602 5 75 miles. b. The islands and

the port form a triangle where the ships’ current locations are midpoints of two sides, making the shortest path between the ships a midsegment of the triangle. The shortest distance between the islands is parallel to this side and twice as long, so the distance is 150 miles. c. 60 miles; 75 miles; 45 miles

SAT/ACT Chapter Test

1. A 2. B 3. E 4. C 5. D 6. A 7. D 8. A

9. B 10. C 11. E 12. 18 13. 41

Performance Assessment

1. Complete answers should include: an explanation that a coordinate proof involves placing geometric fi gures in a coordinate plane; an explanation that when variables are used to represent the coordinates of a fi gure in a coordinate proof, the results are true for all fi gures of the given type; an example of a coordinate proof; an explanation that an indirect proof involves the assumption that the desired conclusion is false and that this original assumption must be shown to be impossible; an example of an indirect proof.

2. a. (65, 50) and (100, 50) b. 35 units c. No. Because the triangle is obtuse, the circumcenter will lie outside of the rose garden. d. about (70, 30) e. about (20, 110) f. about (177, 110) g. The length of the third side must be less than 7 feet and greater than 1 foot.

Chapter 6Quiz 1

1. x 5 6 2. s 5 15 3. a 5 10 4. 9 } 7

5. 8 } 12

or 2 }

3 6.

y 1 7 } 7 7. 11.2

Quiz 2

1. 2 : 1 2. 18 3. 28 4. 122 5. 164, 82

6. 1, 2, 3, 5 7. 2 }

1 5 2,

3 }

2 5 1.5,

5 }

3 ø 1.667

8. similar; n ABC , nDEF 9. not similar

10. similar; nPQR , nTSR

Quiz 3

1. 27 2. 20 3. 42

4.

x

y

1

1

5. x

y

222

Chapter Test A

1. 17

} 2 2.

4 }

1 3.

8 }

1 4.

40 }

1 5. x 5 24 6. x 5 14

7. x 5 1 8. x 5 5 9. 12 10. 20 11. 6 Ï}

10

12. 15 13. 18 14. similar; JKLM , PQRS, 2 } 5

15. similar; nTUV , nXYZ, 4 }

3

16. similar; nABC , nGFH 17. not similar

18. not similar 19. similar; nDHG , nFHE

20. x 5 12 21. x 5 24 22. x 5 28 23. x 5 26

24. 3 25. 1 } 10

26. length 5 140 m, width 5 80 m

Chapter Test B

1. 5 : 1 2. 20

} 1 3.

528 }

1 4.

9 }

1 5. 30 : 1 6.

3 }

1

7. 4.5 8. 5 9. 5 10. 24

11. nABD , nECD; AA Similarity Postulate

12. no 13. 22.5 14. 95 15. 1.5 16. 12

17. 2 18. 1 } 12

19. 8 in., 4 in. 20. 26 in., 6.5 in. 21. 5 ft

Chapter Test C

1. 4 }

9 2.

1 } 5 3.

24 }

1 4. x 5 14 5. x 5 24

6. x 5 7 7. 39

} 5 8. 320

} 31

9. 4 m 10. 8 } 5

11. 11 1 } 5 12. LM 5 8.1, PQ 5 13.0

13. 55, 89, 144, 233

14. 89

} 55 ø 1.6182, 144

} 89

ø 1.6179, 233

} 144

ø 1.6181

15. similar; nABE , nCBD 16. not similar

17. similar; nJKL , nJMN

18. similar; nEHD , nGHF

19. x 5 16 20. x 5 7

Chapter 5, continuedA

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A11Geometry

Assessment Book

21. 22.

x

y

3

1

A9(22, 21)

D9(22, 1)

( )12 B9 21, 2

( )12C9 2 , 1

x

y

1

4A9(0, 0) D9(9, 0)

B9(0, 4.5) C9(4.5, 4.5)

23. $369

Standardized Test A

1. B 2. A 3. C 4. D 5. B 6. C 7. A 8. D

9. B 10. C 11. B 12. C 13. B 14. C

15. C 16. 37.5 17. 20 inches; 1 : 15; 1 : 20

18. a. The 16 3 20 and the 20 3 30 both have a ratio of 1 : 40. b. The 16 3 20 is an enlargement by a scale factor of 2 of the 8 3 10. The 20 3 30 is an enlargement by a scale factor of 5 of the 4 3 6. c. 2 in. 3 3 in. d. Use a scale factor of

1 } 5

for a reduction of the 20 3 30, or use a scale fac-tor of 2 for an enlargement of the wallet size.

Standardized Test B

1. D 2. B 3. A 4. C 5. A 6. D 7. D

8. B 9. C 10. C 11. B 12. B 13. D

14. A 15. D 16. 195 17. length is 1 : 1, width is 1 : 16, area is 1 : 16; After 5 folds: length is 1 : 1, width is 1 : 32, area is 1 : 32; After 6 folds; length is 1 : 1, width is 1 : 64, area is 1 : 64

18. a. A, B, C, E b. The 16 3 20 is an enlargement dilation of the 8 3 10 by a scale factor of 2 : 1. The 10 3 14 is an enlargement dilation of the 5 3 7 by a scale factor of 2 : 1. The 4 3 6 is an enlargement dilation of the 2 3 3 by a scale factor of 2 : 1. The 12 3 16 is an enlargement dilation of the 1.5 3 2 by a scale factor of 8 : 1 c. C and E could print on a 10 3 14. G, I, and J could print on a 6 3 8.

Standardized Test C

1. D 2. B 3. D 4. A 5. D 6. B 7. D 8. A

9. C 10. D 11. B 12. D 13. C 14. C

15. C 16. 30.4 17. 9 ft by 33 ft; 297 ft2

18. a. The 5 3 7 has a ratio of 3 : 35. b. The

4 3 6 is a reduction by a scale factor of 1 }

6 of the

24 3 36. The 8 3 10 is a reduction by a scale

factor of 1 }

2 of the 16 3 20. c. (14, 10) d. 1 }

5

SAT/ACT Chapter Test

1. B 2. C 3. D 4. A 5. E 6. D 7. D 8. C

9. B 10. B 11. A 12. 40 13. 5 ft

Performance Assessment

1. Complete answers should include:

C(6, 2)x

y

2

12

N(18, 6)L(6, 6)

A(2, 2)

F(3, 1)

E(2, 3)

B(4, 6)

D(1, 1)

M(12, 18)

AB

} DE 5 BC

} EF 5 AC

} DF 5 2, so n ABC , nDEF;

AB

} LM 5 BC

} MN 5 AC

} LN 5 1 }

3 , so n ABC , nLMN;

DE

} LM 5 EF

} MN 5 DF

} LN 5 1 }

6 , so nDEF , nLMN.

2. a. about 13 ft by 9 ft b. Because ∠A and ∠C are right angles, ∠A > ∠C. By the Refl exive Property, ∠E > ∠E. So n ABE and nCDE are similar by the AA Similarity Postulate. c. 1.5

d. LF

} FB 5 LM

} ME e. Show that LJ

} LN = LH

} LI . Then

use the Refl exive Property and the SAS Similarity Theorem to show that the triangles are similar.

Chapters 1–6Cumulative Test

1. point D 2. @##$ AB 3. no 4. yes 5. plane ECD and plane ECB 6. 12.6; (21, 22)

7. 11.7; 1 2 1 } 2 , 25 2 8. decagon, equilateral

9. quadrilateral, equilateral 10. 16 m

11. 12.5 ft 12. 9.75 in. 13. 12, 3, 0.75

14. 214, 224, 236 15. If you are not a politician, then you are not a senator.; true

16. m∠ H 5 m∠ G 17. ∠ D > ∠ E

18. x 5 55, y 5 48 19. x 5 5, y 5 16

20. alternate interior 21. alternate exterior

22. consecutive interior 23. corresponding

24. alternate exterior 25. alternate interior

26. yes; Alternate Interior Angles Theorem

27. yes; Corresponding Angles Converse

28. 4 }

3 29. 23 30.

1 }

13 31. y 5 22x 1 3

Chapter 6, continuedA

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