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Name———————————————————————— Date —————————————
Practice B
Lesson
6.3
For use with the lesson “Prove Triangles Similar by AA”
Use the diagram to complete the statement.
1. n ABC ,    ?   
CA
?
AB
2.​ }   ​5 }
​ EF   ​ 5 }
​  ?    ​
?
3. ∠ B >    ?   
8
?
4.​ }  ​ 5 }
​ ? ​
12
5. x 5    ?   
6. y 5    ?   
A
6
x
C
B
8
D
16
12
y
F
E
Determine whether the triangles are similar. If they are, write a
similarity statement.
7.
Y
X
8.
J
M
638
358
A
358
N
P
478
738
L
K
438
C
B
9.
J
458
858
K
Z
P
J
X
L 858
11.
10.
K
N
L
508
M
Y
508
12. G
M
Lesson 6.3
T
6-32
K
Q 458
R
858
N
S
H
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Z
Geometry
Chapter Resource Book
CS10_CC_G_MECR710761_C6L03PB.indd 32
4/28/11 11:55:04 AM
Name———————————————————————— Lesson
6.3
Date —————————————
Practice B continued
For use with the lesson “Prove Triangles Similar by AA”
13. Multiple Choice In the diagram at the right, A
}
find the length of ​BC​ .
B
4
28
A. ​ }  ​
5
B. 6
C. 3
20  ​
D.​ } 
7
C
7
5
D
E
In Exercises 14–17, use the diagram at the right.
A
B
14. List three pairs of congruent angles.
C
15. Name two pairs of similar triangles and write a
similarity statement for each.
D
16. Is n ACD , nBCE ?
E
17. Is nAED > nEAB?
In Exercises 18–21, use the diagram at the right. Find the coordinates of point Z so that nRST , nRXZ.
y
S
18. R(0, 0), S(0, 4), T(28, 0), X(0, 2), Z(x, y)
X
T
Z
R
20. R(0, 0), S(0, 10), T(220, 0), X(0, 6), Z(x, y)
x
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.
}
}
}
}
​  are the legs of the first triangle. DE​
​  and EF​
​  are the legs of the second
​AB​ and BC​
triangle. Which of the following is false?
A. ∠ A > ∠ D
AB
AC
C.​ }  ​ 5 }
​ DE  ​ 
DF
B. AC 5 DF
In Exercises 23–25, use the following information.
Flag Pole In order to estimate the height h of a flag 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.
D
h
B
23. Why are the two overlapping triangles similar?
24. Using the similar triangles, write a proportion
that models the situation.
Lesson 6.3
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
19. R(0, 0), S(0, 6), T(26, 0), X(0, 2), Z(x, y)
A
C
6 ft
5 ft
12 ft
E
25. What is the height h (in feet) of the flag pole?
Geometry
Chapter Resource Book
CS10_CC_G_MECR710761_C6L03PB.indd 33
6-33
4/28/11 11:55:05 AM
}
answers
22. You are given that ​DE​ is a midsegment of
}i}
​  by the Midsegment Thm.,
n ABC. Then DE​
​   AC​
which means that ∠ A > ∠ BDE and ∠ C > ∠ BED
by the Corr. Angles Post. Therefore,
n ABC , n DBE by the AA Similarity Post.
1
23. 37 ​ } ​ft
3
Practice Level B
1. nDEF 2. DE, BC, FD 3. ∠ E 4. x, y
9
64
5. }
​ 2 ​ 6. }
​ 3  ​ 7. n ABC , 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,
n ABD , nEDB 16. no 17. yes 18. (4, 0)
1 
2
36
19. (2, 0) 20. (12, 0) 21. ​ }
​ 7  ​, 0  ​ 22. B
23. Both triangles are right triangles and have
∠ A in common. Because both triangles have two
congruent angles, the triangles are similar.
18
h
24. }
​ 5 ​5 }
​ 6  ​ 25. 15 ft
1. similar 2. cannot be determined 3. similar
4. not enough information
s
5. n LMN , n HGD; both are 188-728-908 n
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 ?.
}
​Ï149 ​ 
1
2
10. x 5 5, y 5 }
​  2   
​  11. x 5 3 ​ }3 ​, y 5 4 ​ }3 ​
12. not possible: can’t be sure the triangles are
}
4​Ï306 ​ 
similar 13. x 5 }
​  3   
​, y 5 12 14. no 15. yes
16. no 17. (6, 4), (6, 24) 18. (0, 9), (0, 29)
2 1 
2
36
54 36 54
19. ​ }
​ 13 ​, }
​ 13 ​   ​, ​ }
​ 13 ​, 2​ }
 ​   ​ 20. (0, 4), (0, 24)
13
A82
Geometry
Chapter Resource Book
2 1 
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 ? Congruence 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
s are
parallel. This leads to > alt. int. ?. Then the n
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.
Practice Level C
1 
1 
36
24 36 24
21. (6, 9), (6, 29) 22. ​ }
​ 13 ​,  }
​ 13 ​  ​, ​ }
​ 13 ​,  2​ }
 ​   ​
13
Interdisciplinary Application
1.
C
A
12 in.
D
14 in.
E
1
in.
4
B
Not drawn to scale
}
}
2. ​BC​  3. AB​
​   4. 56 ft 5. 288 ft
Challenge Practice
1.
Statements
1. ∠ A ù ∠ BCD
2. ∠ BCA and ∠ ADC
are right angles.
3. ∠ BCA ù ∠ ADC
Reasons
1. Given
2. Given
3. Right Angle
Congruence
Theorem
4. n ABC , n ACD 4. AA Similarity
Postulate
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Lesson 6.3 Prove Triangles
Similar by AA, continued
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