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Five-Minute Check (over Chapter 7)
CCSS
Then/Now
New Vocabulary
Key Concept: Geometric Mean
Example 1: Geometric Mean
Theorem 8.1
Example 2: Identify Similar Right Triangles
Theorems: Right Triangle Geometric Mean Theorems
Example 3: Use Geometric Mean with Right Triangles
Example 4: Real-World Example: Indirect Measurement
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Solve the proportion
The triangles at the right
are similar. Find x and y.
Determine whether the
triangles at right are
similar. If so, write a
similarity statement.
Find the perimeter of ∆DEF if ∆ABC ~ ∆DEF,
AB = 6.3, DE = 15.75, and the perimeter of ∆ABC is
26.5.
Over Chapter 7
Solve the proportion
A. 15
B. 16.5
C.
D. 18
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Over Chapter 7
The triangles at the right
are similar. Find x and y.
A. x = 16.1, y = 1.6
B. x = 15.6, y = 2.1
C. x = 7.8, y = 8.4
D. x = 17.6, y = 3.7
Over Chapter 7
Determine whether the triangles are similar. If so,
write a similarity statement.
A. yes, ∆ABC ~ ∆EDF
B. yes, ∆ABC ~ ∆DEF
C. yes, ∆ABC ~ ∆EFD
D. No, sides are not
proportional.
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Over Chapter 7
Find the perimeter of ∆DEF if ∆ABC ~ ∆DEF,
AB = 6.3, DE = 15.75, and the perimeter of ∆ABC is
26.5.
A. 66.25
B. 64.5
C. 12.4
D. 10.6
Over Chapter 7
Figure JKLM has a perimeter of 56 units. After a
dilation with a scale factor of 2, what will the
perimeter of figure J'K'L'M' be?
A. 28 units
B. 54 units
C. 58 units
D. 112 units
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Content Standards
G.SRT.4 Prove theorems about triangles.
G.SRT.5 Use congruence and similarity
criteria for triangles to solve problems and to
prove relationships in geometric figures.
Mathematical Practices
7 Look for and make use of structure.
3 Construct viable arguments and critique
the reasoning of others.
You used proportional relationships of
corresponding angle bisectors, altitudes, and
medians of similar triangles.
• Find the geometric mean between two
numbers.
• Solve problems involving relationships
between parts of a right triangle and the
altitude to its hypotenuse.
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• geometric mean
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Geometric Mean
Find the geometric mean between 2 and 50.
Let x represent the geometric mean.
Answer: The geometric mean is 10.
A. Find the geometric mean between 3 and 12.
A. 3.9
B. 6
C. 7.5
D. 4.5
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Identify Similar Right Triangles
Write a similarity statement identifying the three
similar triangles in the figure.
Separate the triangles
into two triangles along
the altitude.
Notice
Answer: So, by Theorem 8.1, ∆EGF ~ ∆FGH ~ ∆EFH.
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Write a similarity statement identifying the three
similar triangles in the figure.
A. ∆LNM ~ ∆MLO ~ ∆NMO
B. ∆NML ~ ∆LOM ~ ∆MNO
C. ∆LMN ~ ∆LOM ~ ∆MON
D. ∆LMN ~ ∆LMO ~ ∆MNO
Δ Δ
=
Δ Δ
Δ Δ
=
Δ Δ
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Use Geometric Mean with Right Triangles
Find c, d, and e.
12 5
6 5
12
Find e
c
d
==
6
30 %
==
% 24
24
30
% = 6
24• •24
30
30
% = 144
720
180
%=
= 12720
180
% = 12
6 55
Find e to the nearest tenth.
A. 13.9
B. 24
C. 17.9
D. 11.3
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