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Name ——————————————————————— Date ————————————

Practice BFor use with the lesson “Prove Triangles Similar by AA”

Use the diagram to complete the statement.

16

8

6

12

A

C B

x

yF

D

E

1. n ABC , ? 2. AB

} ? 5

? } EF 5

CA } ?

3. ∠ B > ? 4. ? }

12 5

8 } ?

5. x 5 ? 6. y 5 ?

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

7.

438

478

A

CB

X Y

Z

8.

738

638358

358

J

KL

M

P

N

9.

508

458

858858L

Z

K

J

Y

X

10.

L M

J

K N

11. P

Q

R

T

S

508

458

858

12. G

H

K

M

N

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GeometryChapter Resource Book6-32

Lesson

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CS10_CC_G_MECR710761_C6L03PB.indd 32 4/28/11 11:55:04 AM

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13. Multiple Choice In the diagram at the right, A B

C

ED

4

5 7

find the length of

} BC .

A. 28 } 5 B. 6

C. 3 D. 20 } 7

In Exercises 14–17, use the diagram at the right.

D

A B

E

C 14. List three pairs of congruent angles.

15. Name two pairs of similar triangles and write a similarity statement for each.

16. Is n ACD , nBCE?

17. Is nAED > nEAB?

In Exercises 18–21, use the diagram at the right.

x

y

S

X

R Z T

Find the coordinates of point Z so that nRST , nRXZ.

18. R(0, 0), S(0, 4), T(28, 0), X(0, 2), Z(x, y)

19. R(0, 0), S(0, 6), T(26, 0), X(0, 2), Z(x, y)

20. R(0, 0), S(0, 10), T(220, 0), X(0, 6), Z(x, y)

21. R(0, 0), S(0, 7), T(29, 0), X(0, 4), Z(x, y)

22. Multiple Choice Triangles ABC and DEF are right triangles that are similar. }

AB and }

BC are the legs of the first triangle. } DE and } EF are the legs of the second triangle. Which of the following is false?

A. ∠ A > ∠ D B. AC 5 DF C. AC

} DF 5 AB

} DE

In Exercises 23–25, use the following information.

Flag Pole In order to estimate the height h of a flag

12 ft

h

6 ftA

B

CE

D

5 ft

pole, a 5 foot tall male student stands so that the tip of his shadow coincides with the tip of the flag pole’s shadow. This scenario results in two similar triangles as shown in the diagram.

23. Why are the two overlapping triangles similar?

24. Using the similar triangles, write a proportion that models the situation.

25. What is the height h (in feet) of the flag pole?

Practice B continuedFor use with the lesson “Prove Triangles Similar by AA”

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GeometryChapter Resource Book 6-33

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CS10_CC_G_MECR710761_C6L03PB.indd 33 4/28/11 11:55:05 AM

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Lesson Prove Triangles Similar by AA, continued22. You are given that } DE is a midsegment of n ABC. Then } DE i } AC by the Midsegment Thm., which means that ∠ A > ∠ BDE and ∠ C > ∠ BED by the Corr. Angles Post. Therefore, n ABC , n DBE by the AA Similarity Post.

23. 37 1 }

3 ft

Practice Level B

1. nDEF 2. DE, BC, FD 3. ∠E 4. x, y

5. 9 }

2 6.

64 }

3 7. nABC , nZYX 8. not similar

9. nJLK , nYXZ 10. nJNK , nJML

11. nPTQ , nPRS 12. nKGH , nKNM

13. D 14. Sample answer: ∠BAE > ∠DEA, ∠DCA > ∠BCE, ∠ADB > ∠EBD

15. Sample answer: nCAB , nCED, nABD , nEDB 16. no 17. yes 18. (4, 0)

19. (2, 0) 20. (12, 0) 21. 1 36 } 7 , 0 2 22. B

23. Both triangles are right triangles and have ∠A in common. Because both triangles have two congruent angles, the triangles are similar.

24. h } 5 5

18 } 6 25. 15 ft

Practice Level C

1. similar 2. cannot be determined 3. similar

4. not enough information

5. n LMN , n HGD; both are 188-728-908 ns

6. n XTR , n KAJ by the AA Similarity Post.

7. n QNM , n PNO by the AA Similarity Post.

8. n ABC , n EDC; The vertical angles are >, so the AA Similarity Post. applies.

9. n RSV , n RTU; ∠ R > ∠ R and there are two pairs of > corresponding ?.

10. x 5 5, y 5 Ï}

149 }

2 11. x 5 3

1 }

3 , y 5 4

2 }

3

12. not possible: can’t be sure the triangles are

similar 13. x 5 4 Ï

}

306 }

3 , y 5 12 14. no 15. yes

16. no 17. (6, 4), (6, 24) 18. (0, 9), (0, 29)

19. 1 54 }

13 ,

36 }

13 2 , 1 54

} 13

, 2 36

} 13 2 20. (0, 4), (0, 24)

21. (6, 9), (6, 29) 22. 1 24 }

13 ,

36 }

13 2 , 1 24

} 13

, 2 36

} 13 2 23. You are given that ∠ CAB is a right ∠ and }

AD is an altitude. Then }

AD ⊥ }

BC by the def. of altitude. So, ∠ CDA is a right ∠ because if two lines are ⊥ , they intersect to form four right ?. Because all right ? are >, ∠ CAB > ∠ CDA. You know that∠ ACD > ∠ ACD by the Reflexive Prop. of >. Therefore, n ABC > n DAC by the AA Similarity Post.

24. You are given }

AC i } GE and }

BG i } CF . Then ∠ A > ∠ E and ∠ EDF > ∠ EHG by the Corr. ? Post. But, ∠ EHG > ∠ AHB by the Vertical ? Congru-ence Thm. So, ∠ EDF > ∠ AHB by the Transitive Prop. of >. Therefore, n ABH , n EFD by the AA Similarity Post. 25. 900,000 km; The dashed line is perpendicular to the bases of the two triangles, so those bases are parallel. This leads to > alt. int. ?. Then the ns are similar by AA and you can form a proportion to estimate the Sun’s diameter.

Study Guide 1. yes; nCDE , nGFE

2. yes; nPQR , nLMN 3. not similar

4. yes; nXYZ , nPQZ 5. 80 ft

6. About 68 in. or 5 ft 8 in.

Interdisciplinary Application 1.

A

C

B

D

E

1 4 in.

12 in. 14 in.

Not drawn to scale

2. }

BC 3. }

AB 4. 56 ft 5. 288 ft

Challenge Practice 1.

Statements Reasons

1. ∠ A ù ∠ BCD 1. Given2. ∠ BCA and ∠ ADC 2. Given

are right angles.3. ∠ BCA ù ∠ ADC 3. Right Angle

Congruence Theorem

4. nABC , nACD 4. AA Similarity Postulate

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GeometryChapter Resource BookA82

6.3