LMN or RST ABC - Mr. Walker

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

Practice B

Lesson

6.4

Lesson 6.4

Date ¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

For use with the lesson ¡°Prove Triangles Similar by SSS and SAS¡±

Is either nLMN or nRST similar to n ABC?

A

1.

L

10

10

B

8

M

C

12

R

5

6

N

8

2.

S

S

A

8

M

9

B

10

5

4

4.5

T

6

6

N

R

12

9

L

C

5

T

Determine whether the two triangles are similar. If they are similar, write

a similarity statement and find the scale factor of n A to nB.

J

3 A

858

L

X

4.

J

X

4

K

16

858

B

Z

18

10

12

A

B

9

L

K

Y

16

Z

Y

Not drawn to scale

5. Algebra Find the value of m that makes n ABC , nDEF when AB 5 3, BC 5 4,

DE 5 2m, EF 5 m 1 5, and ¡Ï B > ¡Ï E.

Show that the triangles are similar and write a similarity statement.

Explain your reasoning.

6.

P

R

6-46

8

3.5

T

6

Q

2

7. G

4

K

8

5

7

H

10

S

4

M

N

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3.

Geometry

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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

Lesson

6.4

Date ¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

Practice B

continued

For use with the lesson ¡°Prove Triangles Similar by SSS and SAS¡±

8. Multiple Choice In the diagram at the right,

A. 12

B. 18

35

C.???}?

2

30

D. ??}?

7

Lesson 6.4

A

}

n ACE , nDCB. Find the length of AB?

? .

B

10

C

14

D 6 E

Sketch the triangles using the given description. Explain whether the two

triangles can be similar.

9. The side lengths of n ABC are 8, 10 and 14.

10. In n ABC, AB 5 15, BC 5 24 and m¡Ï B 5 38¡ã.

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

The side lengths of nDEF are 16, 20 and 26. In nDEF, DE 5 5, EF 5 8 and m¡Ï E 5 38¡ã.

In Exercises 11¨C14, use the diagram at the right

to copy and complete the statement.

A

B

14

11. n ABC , ???????

C 1358

12. m¡Ï DCE 5 ???????

13. AB 5 ???????

16

14. m¡Ï CAB 1 m¡Ï ABC 5 ???????

D

12

E

In Exercises 15 and 16, use the following information.

Pine Tree In order to estimate the height h of a tall

pine tree, a student places a mirror on the ground and

stands where she can see the top of the tree, as shown.

The student is 6 feet tall and stands 3 feet from the

mirror which is 11 feet from the base of the tree.

h

15. What is the height h (in feet) of the pine tree?

16. Another student also wants to see the top of the

tree. The other student is 5.5 feet tall. If the

mirror is to remain 3 feet from the student¡¯s feet,

how far from the base of the tree should the

mirror be placed?

6 ft

3 ft

11 ft

Geometry

Chapter Resource Book

CS10_CC_G_MECR710761_C6L04PB.indd 47

6-47

4/28/11 11:33:01 AM

10.

24

F

RS

6

4

2 ST

2

5. }

??XY ?5 }

??6?5 }

??3?, }

??YZ?5 }

??9 ?5 }

??3 ?, so two pairs of sides

are proportional. Because the included angles

¡Ï S and ¡Ï Y are right angles, they are congruent.

Therefore, n RST , n XYZ by SAS Similarity

2

Thm.; scale factor: }

??3 ?

7

28

7 ST

RT

21

6. }

??XZ?5 }

??16 ?5 }

??4 ?, }

??YZ ?5 }

??12 ?5 }

??4 ?, so two pairs of

sides are proportional, and their included angles

are congruent (¡Ï T > ¡Ï Z). Therefore,

n RST , n XYZ by SAS Similarity Thm.;

7

9

scale factor: }

??4 ? 7. n JKL , n TUV; }

??5? 8. no

5

9. yes; n CDG , n CEF; }

??9 ? 10. no

16.

17.

3

Y

A

60

388

388

B

15

5

D

Practice Level C

1. yes; n ABC , nDEC by AA 2. no 3. yes;

n LMN , nDMP by SAS

4. Mark DF as 30 to use SSS.

5. Mark m¡Ï J as 798 to use SAS.

4

6. Mark UV as 44???}?to use SAS.

9

7.

A

E

A

8

n ABC , nDEF; SAS Similarity Theorem

11. nEDC 12. 458 13. 10.5

14. 1358 15. 22 ft 16. 12 ft

8.

8

8




11. yes; SSS Similarity Thm. 12. yes; SAS

Similarity Thm. 13. no 14. yes; SSS Similarity

Thm. 15. yes; AA Similarity Post.

X

C

??

?n

?{




{n

9

<

?{

X

?x

??

9

15

AA Similarity Post. SAS Similarity Thm.

6

80

80

60

12

B

B

C

C

Y

85

Z

SAS Similarity Thm AA Similarity Post.

18. a. AA Similarity Post. b. Sample answer:

Use the similar triangles to set up the proportion

9.

SAS Similarity Thm.

X

2

A

Y

50

4.5

Z

4

B

50

C

9

28

l

}

??10 ?5 }

??8 ?; 35 ft

10. 458 11. 858 12. 10 13. 10?? 2??

Practice Level B

14. 10 1 ?

? 69?? 15. n ABD , n GFD,

}

}

1. nRST 2. nLMN 3. nJLK , nYXZ; 1 : 4

4. not similar 5. 3 6. nPQT , nPSR;

SSS Similarity Theorem 7. nKNM , nKGH;

SAS Similarity Theorem 8. B

9.

D

A

14

C

10

8

B

26

F

20

16

E

n ABC cannot be similar to nDEF because not all

corresponding sides are proportional.

n CBD , n EFD, n ACD , n GED

16. x 5 10, y 5 5 17. x 5 76, y 5 5

1

18. x 5 8, y 5 4, z 5 2???}?

3

19. Sample answer: You are given that n ABC is

equilateral, so AB 5 BC 5 AC by the

definition of an equilateral n. It is given that

1

} }

}

DE?

? , DF?

? , and EF?

? are midsegments, so DE 5 }

??2??BC,

1

1

EF 5 ??}2 ??AC, and DF 5 ??}2 ??AB by the midsegment

1

1

??2 ??BC, and

Thm. Then DE 5 ??}2??BC, EF 5 }

1

DF 5 }

??2??BC by the Substitution Property of

A84

<

??

Z

6

??

?x

Geometry

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

answers

Lesson 6.4 Prove Triangles

Similar by SSS and SAS,

continued

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