474 Chapter 7 Similarity

ExercisesExercises7-3KEYWORD: MG7 7-3

KEYWORD: MG7 Parent

GUIDED PRACTICE

SEE EXAMPLE 1 p. 470

Explain why the triangles are similar and write a similarity statement.

1. 2.

SEE EXAMPLE 2 p. 471

Verify that the triangles are similar.

3. �DEF and �JKL 4. �MNP and �MRQ

SEE EXAMPLE 3 p. 471

Multi-Step Explain why the triangles are similar and then find each length.

5. AB 6. WY

SEE EXAMPLE 4 p. 472

7. Given: �

�

MN ‖ −−

KL 8. Given: SQ = 2QP, TR = 2RP

Prove: �JMN ∼ �JKL Prove: �PQR ∼ �PST

9. The coordinates of A, B, and C are A(0, 0), B(2, 6), and C(8, -2). What theorem or postulate justifies the statement �ABC ∼ �ADE, if the coordinates of D and E are twice the coordinates of B and C?

SEE EXAMPLE 5 p. 472

10. Surveying In order to measure

533 m

733 m

800 m

586 m

644 m

C

S

A

D

B

the distance AB across the meteorite crater, a surveyor at S locates points A, B, C, and Das shown. What is AB to the nearest meter? nearest kilometer?1200 m, or 1.2 km

SAS or SSS ∼ Thm.

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474 Chapter 7

7-3 ExercisesExercises

KEYWORD: MG7 Resources

Assignment Guide

Assign Guided Practice exercises as necessary.

If you finished Examples 1–3 Basic 11–16, 20–24, 31 Average 11–16, 19–24, 27, 31 Advanced 11–16, 20–24, 27, 31,

37, 40

If you finished Examples 1–5 Basic 11–19, 23–25, 32–37,

41–46 Average 11–25, 29–37, 41–46 Advanced 11–20, 23–28, 30, 31,

33–46

Homework Quick CheckQuickly check key concepts.Exercises: 11, 12, 14, 16, 18, 23

Answers 1. By the � Sum Thm., m∠ A =

47°. So by the def. of �, ∠ A �∠F, and ∠C � ∠H. Therefore � ABC ∼ �FGH by AA ∼.

2. It is given that ∠P � ∠T. ∠QST is a rt. ∠ by the Lin. Pair Thm., so ∠QST � ∠RSP. Therefore �QST∼ �RSP by AA ∼.

3. DF_JL

=DE_JK

=EF_KL

=1_2 , so �DEF

∼ � JKL by SSS ∼.

4. It is given that ∠NMP �∠RMQ. MN___

MR = MP___MQ = 2__

3 . Therefore �MNP ∼ �MRQ by SAS ∼.

5. It is given that ∠ AED � ∠ ACB. ∠ A � ∠ A by the Reflex. Prop. of �. Therefore � AED ∼ � ACB by AA ∼. AB = 10

6–8. See p. A23.

37°37°

12 24

18

12

9

6

20

16

8 10

7-3 PRACTICE A

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5 ft 5 in.4 ft 6 in.

15 in.

7- 3 Triangle Similarity: AA, SSS, and SAS 475

PRACTICE AND PROBLEM SOLVING

For See Exercises Example

11–12 1 13–14 2 15–16 3 17–18 4 19 5

Independent Practice Explain why the triangles are similar and write a similarity statement.

11. 12.

Verify that the given triangles are similar.

13. �KLM and �KNL 14. �UVW and �XYZ

Multi-Step Explain why the triangles are similar and then find each length.

15. AB 16. PS

17. Given: CD = 3AC, CE = 3BC 18. Given: PR_MR

= QR_NR

Prove: �ABC ∼ �DEC Prove: ∠1 � ∠2

19. Photography The picture shows a person taking a pinhole photograph of himself. Light entering the opening reflects his image on the wall, forming similar triangles. What is the height of the image to the nearest tenth of a foot?

Draw �JKL and �MNP. Determine if you can conclude that �JKL ∼ �MNP based on the given information. If so, which postulate or theorem justifies your response?

20. ∠K � ∠N, JK_

MN= KL_

NP21.

JK_MN

= KL_NP

= JL_

MP22. ∠J � ∠M,

JL_MP

= KL_NP

Find the value of x.

23. 24.

Skills Practice p. S16Application Practice p. S34

Extra Practice

11. It is given that ∠GLH � ∠K.∠G � ∠G by the Reflex. Prop. of �.Therefore �HLG ∼�JKG by AA ∼.

12. By the Isosc. � Thm., ∠C � ∠B.By the � Sum Thm. m∠C = m∠B = 74°. In the same way, m∠F = 74°. So by the def. of �,∠B � ∠E and ∠C � ∠F. Therefore �ABC ∼ �DEFby AA ∼.

13. ∠K � ∠K by the Reflex. Prop. of �. KL___

KN= KM___

KL= 3__

2 .

Therefore �KLM ∼�KNL by SAS ∼.

14. UV___XY

= VW___YZ

= WU___ZX

= 8__11

. Therefore �UVW ∼�XYZ by SSS ∼.

1.5 ft

yes; SAS ∼ yes; SSS ∼no

3 7

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Lesson 7-3 475

A common error in Exercise 16 is to let PS = x and then to write and solve the proportion x__

6 = 10____17.5 . Point

out that 6 is not the length of a side of any triangle, so it cannot be used in the proportion. Encourage students to draw �PST and �PVWseparately and then write the correct proportion, x_____

x + 6 = 10____17.5 .

Algebra In Exercise 16,remind students that in any proportion such

as x_____x + 6 = 10____

17.5 , they should use parentheses to write the product as 10(x + 6). Then use the Distributive Property to remove the parentheses.

Answers 15. It is given that ∠ ABD � ∠C. ∠ A

� ∠ A by the Reflex. Prop. of �. Therefore � ABD ∼ � ACB by AA ∼. AB = 8

16. Since −−ST ‖

−−VW , ∠PST � ∠V by

the Corr. � Post. ∠P � ∠P by the Reflex. Prop. of �. Therefore �PST ∼ �PVW by AA ∼. PS = 8

17. 1. CD = 3AC, CE = 3BC (Given)

2. CD_AC

= 3, CE_BC

= 3 (Div. Prop.

of =) 3. ∠ ACB � ∠DCE (Vert. � Thm.) 4. � ABC ∼ �DEC (SAS ∼ Steps

2, 3)

18. 1. PR___MR =

QR___NR (Given)

2. ∠R � ∠R (Reflex. Prop. of �) 3. �PQR ∼ �MNR (SAS ∼ Steps

1, 2) 4. ∠1 � ∠2 (Def. of ∼ �)

4

372

7-3 PRACTICE C

16

82412

1.8

3.6 3 3.5

6

2.1

5

1.253.25

7-3 PRACTICE B

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