Name———————————————————————— Date —————————————
Practice B
Lesson
7.3
For use with the lesson “Use Similar Right Triangles”
Complete and solve the proportion.
?
x  ​5 }
1.​ } 
​ 8 ​
12
15
x
2.​ }  ​5 }
​ ? ​
x
9
x
3.​ } ​5 }
​ ? ​
x
11
x
12
x
9
15
8
20
x
Find the value(s) of the variable(s).
4.
5.
a
6.
x
12
10
6
6
7.
8.
8
y
16
w19
z
9.
c
32
x
18
a
b
24
14
Tell whether the triangle is a right triangle. If so, find the length of the
altitude to the hypotenuse. Round decimal answers to the nearest tenth.
10.
11.
6 19
12.
18
2 85
12
30
15
19
6 34
14
Use the Geometric Mean Theorems to find AC and BD.
13.
D
A
40
30
A
14.
15.
B
C
35
10
B
6
C
B
D
C
5
D
Geometry
Chapter Resource Book
A
Lesson 7.3
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
8
24
b
7-37
Name———————————————————————— Lesson
7.3
Date —————————————
Practice B continued
For use with the lesson “Use Similar Right Triangles”
16. Complete the proof.
GIVEN: n XYZ is a right triangle with m∠ XYZ 5 908.
X
} } }
​  , YU​
​  is an altitude of nXYZ.
​VW​ i XY​
PROVE: nYUZ , nVWZ
Statements
U
Reasons                 
V
}
1. nXYZ is a right n with altitude ​YU​ . 1.    ?   
2. nXYZ , nYUZ 2.    ?   
} }
3. ​VW​ i XY​
​   3.    ?   
Y
W
Z
4. ∠ VWZ > ∠ XYZ 4.    ?   
5. ∠ Z > ∠ Z 5.    ?   
6.    ?    6. AA Similarity Postulate
7. nYUZ , nVWZ 7.    ?   
In Exercises 17–19, use the diagram.
17. Sketch the three similar triangles in the diagram. K
J
M
18. Write similarity statements for the three triangles.
19. Which segment’s length is the geometric mean of
LM and JM?
Lesson 7.3
20. Kite Design You are designing a diamond-shaped B
kite. You know that AB 5 38.4 centimeters,
BC 5 72 centimeters, and AC 5 81.6 centimeters.
}
You want to use a straight crossbar ​BD​ . About how
long should it be?
A
D
C
7-38
Geometry
Chapter Resource Book
L
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Label the vertices.