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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