Practice B 6.1 For use with the lesson “Use Similar Polygons”

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Date ¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

Practice B

Lesson

6.1

For use with the lesson ¡°Use Similar Polygons¡±

List all pairs of congruent angles for the figures. Then write the ratios of

the corresponding sides in a statement of proportionality.

1. n ABC , nDFE

2. WXYZ , MNOP

A

D

B

W

X

Z

C

Y

M

N

F

E

P

O

3. Multiple Choice Triangles ABC and DEF are similar. Which statement is

AB BC

A.???}?5 }

??EF ?

DE

AB

CA

B.???}?5 }

??DE?

FD

Lesson 6.1

not correct?

C. ¡Ï A > ¡Ï F

Determine whether the polygons are similar. If they are, write a similarity

statement and find the scale factor.

D

4.

5.

Copyright ? Houghton Mifflin Harcourt Publishing Company. All rights reserved.

A

5

6

5

24

W

D

6

16

6

3

C

E

4

A

4

4

6

C

B

X

16

B

F

Z

Y

24

In the diagram, WXYZ , MNOP.

6. Find the scale factor of WXYZ to MNOP.

7. Find the values of x, y, and z.

P

10

8. Find the perimeter of WXYZ.

W

9. Find the perimeter of MNOP.

10. Find the ratio of the perimeter of MNOP to

the perimeter of WXYZ.

12

y

Z

12

z8

Y

M

X

8

O

x

1358

10

N

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6-7

4/28/11 2:10:18 PM

Name¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

Date ¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

Practice B

Lesson

continued

For use with the lesson ¡°Use Similar Polygons¡±

6.1

The two triangles are similar. Find the values of the variables.

11.

12.

n

5.5

6

15

m

10

8

12

m

m?4

In Exercises 13 and 14, use the following information.

Lesson 6.1

Similar Triangles Triangles RST and WXY are similar. The side lengths of nRST are

10 inches, 14 inches, and 20 inches, and the length of an altitude is 6.5 inches. The shortest

side of nWXY is 15 inches long.

13. Find the lengths of the other two sides of nWXY.

14. Find the length of the corresponding altitude in nWXY.

15. Multiple Choice The ratio of one side of n ABC to the corresponding side of a

similar nDEF is 4 : 3. The perimeter of nDEF is 24 inches. What is the perimeter

of n ABC ?

B. 24 inches

C. 32 inches

In the diagram, nXYZ , nMNP.

16. Find the scale factor of nXYZ to nMNP.

X

4

17. Find the unknown side lengths of both triangles.

18. Find the length of the altitude shown in nXYZ.

Z

6

Y

M

19. Find and compare the areas of both triangles.

10

5.8

9

P

In Exercises 20¨C22, use the following information.

Swimming Pool The community park has a rectangular swimming pool enclosed by a

rectangular fence for sunbathing. The shape of the pool is similar to the shape of the fence.

The pool is 30 feet wide. The fence is 50 feet wide and 100 feet long.

20. What is the scale factor of the pool to the fence?

21. What is the length of the pool?

N

Copyright ? Houghton Mifflin Harcourt Publishing Company. All rights reserved.

A. 18 inches

22. Find the area reserved strictly for sunbathing.

6-8

Geometry

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Answers for Chapter 6

Lesson 6.1 Use Similar

Polygons

Practice Level B

Teaching Guide

??}

?5 }

??FE ?5 }

??DE? 2. ¡Ï W > ¡Ï M, ¡Ï X > ¡Ï N,

DF

1. ¡Ï A > ¡Ï D, ¡Ï B > ¡Ï F, ¡Ï C > ¡Ï E,

AB

BC

AC

XY

WX

YZ

WZ

??NO?5 }

??OP?5 }

??MP?

¡Ï Y > ¡Ï O, ¡Ï Z > ¡Ï P, }

??MN?5 }

1

1

3. C 4. no 5. yes; BCDA , WXYZ; ??}?or

4

2

WXYZ , BCDA; 4

3

answers

1.

5

4

6. ??}? 7. 15, 8, 135 8. 40 9. 50 10. }

??4 ?

5

4

11. m 5 11, n 5 4 12. m 5 8 13. 30 in., 21 in.

2

14. 9.75 in. 15. C 16. ??}?

5

17. XY 5 3.6, PN 5 15 18. 2.32

5

19. Area of n XYZ 5 6.96; Area of

nMNP 5 43.5; The ratio of the areas of

similar triangles equals the scale factor squared.

2. 5 pentagons, 20 obtuse isosceles triangles,

25 acute triangles and 1 kite

Practice Level A

1. ¡Ï A > ¡Ï D, ¡Ï B > ¡Ï E, ¡Ï C > ¡Ï F;

BC

AC

AB

??}

?5 }

??EF ?5 }

??DF?

DE

Copyright ? Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Similarity

2. ¡Ï R > ¡Ï W, ¡Ï S > ¡Ï V, ¡Ï T > ¡Ï U;

RS

ST

RT

??}

?5 }

??VU?5 }

??WU?

WV

3. ¡Ï C > ¡Ï M, ¡Ï D > ¡Ï J, ¡Ï E > ¡Ï K,

CD

CF

DE

EF

¡Ï F > ¡Ï L; }

??MJ ?5 ??}

?5 }

??KL?5 }

??ML?

JK

4. ¡Ï P > ¡Ï Z, ¡Ï Q > ¡Ï W, ¡Ï R > ¡Ï X,

PQ

QR

RS

PS

}

¡Ï S > ¡Ï Y; ??}

?

5

??

?5 }

??XY?5 }

??ZY?

ZW

WX

3

1

5. n ABC , n FDE; }

??2 ? 6. GHIJ , KLMN; }

??2 ?

1

7. not similar 8. n ABC , n FDE; }

??1 ? 9. 8

3

10. 18 11. ??}?; P(n LMN) 5 45, P(n PQR) 5 60

4

3

12. }

??5?; P(XYZW) 5 100, P(STUV) 5 60

3

20. }

??5? 21. 60 ft 22. 3200 ft2

Practice Level C

1. ¡Ï S > ¡Ï C, ¡Ï T > ¡Ï D, ¡Ï U > ¡Ï E;

ST

TU

SU

??}

?5 }

??DE?5 }

??CE?

CD

2. ¡Ï L > ¡Ï G, ¡Ï M > ¡Ï H, ¡Ï N > ¡Ï I;

MN

LN

LM

}

??GH?5 }

??HI ?5 }

??GI ?

3. ¡Ï C > ¡Ï M, ¡Ï D > ¡Ï N, ¡Ï E > ¡Ï K,

CD

CF

DE

EF

¡Ï F > ¡Ï L; }

??MN?5 }

??NK?5 }

??KL?5 }

??ML?

4

4. n LNM , n TPO; }

??3 ?

5

5. quadrilateral ABCD , quadrilateral HEFG; }

??8?

3

2

6. ??}? 7. ??}? 8. 4.5 9. 1178 10. 24 11. 201.6 ft

3

2

rv

sv

tv

12. 77.4 in. 13. }

??u ? 14. ??}

? 15. ??}

? 16. 6

u

u

17. 25, 2.5 18. 8 19. 20.4, 15

20. 8 times greater

13. altitudes; x 5 24 14. medians; y 5 12

Study Guide

9

5

1. }

??10 ? 2. 36 3. }

??4? 4. 77.5 5. 20

15. The shadow is not similar to the kite because

the corresponding side ratios are not all the same:

Problem Solving Workshop:

Mixed Problem Solving

95

1. a. 58,800 yen b. about 580.56 Canadian

2

dollars 2. a. ??}7 ?, x 5 45.5, y 5 17.5 b. 50, 175

142

??}

?< 1.22 ? 1.08 ? }

??132 ?

78

Geometry

Chapter Resource Book

A79

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