SOLUTION
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SOLUTION
EXAMPLE 1 Use the SSS Similarity Theorem
Compare ABC and DEF by finding ratios of corresponding side lengths.
Shortest sidesABDE
43
86 ==
Is either DEF or GHJ similar to ABC?
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EXAMPLE 1
Longest sides CAFD
43
1612 ==
Remaining sidesBCEF
43
12 9 ==
Compare ABC and GHJ by finding ratios of corresponding side lengths.
Shortest sides
Use the SSS Similarity Theorem
ABGH
88 == 1
All of the ratios are equal, so ABC ~ DEF.ANSWER
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EXAMPLE 1 Use the SSS Similarity Theorem
Longest sides CAJG
1616 == 1
Remaining sides BCHJ
65
1210 ==
The ratios are not all equal, so ABC and GHJ are not similar.
ANSWER
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SOLUTION
EXAMPLE 2 Use the SSS Similarity Theorem
ALGEBRA
Find the value of x that makes ABC ~ DEF.
STEP 1 Find the value of x that makes corresponding side lengths proportional.
412 = x –1
18 Write proportion.
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EXAMPLE 2 Use the SSS Similarity Theorem
4 18 = 12(x – 1)
72 = 12x – 12
7 = x
Cross Products Property
Simplify.
Solve for x.
Check that the side lengths are proportional when x = 7.
STEP 2
BC = x – 1 = 6
618
412 =
ABDE
BCEF=?
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EXAMPLE 2 Use the SSS Similarity Theorem
DF = 3(x + 1) = 24
824
412 =
ABDE
ACDF=?
When x = 7, the triangles are similar by the SSS Similarity Theorem.
ANSWER
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GUIDED PRACTICE for Examples 1 and 2
1. Which of the three triangles are similar? Write a similarity statement.
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GUIDED PRACTICE for Examples 1 and 2
SOLUTION
Compare MLN and RST by finding ratios of corresponding side lengths.
Shortest sides LM RS
56
2024 ==
Longest sides ST LN
3324=
Remaining sides LN RT
3630 = = 13
15
The ratios are not all equal, so LMN and RST are not similar.
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GUIDED PRACTICE for Examples 1 and 2
Compare LMN and ZYX by finding ratios of corresponding side lengths.
Shortest sides
Remaining sides
Longest sides
LM YZ
23
2030 ==
23=LN
XZ 2639=
MN XZ
2436 = = 2
3
All of the ratios are equal, so MLN ~ ZYX.
ANSWER
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GUIDED PRACTICE for Examples 1 and 2
2. The shortest side of a triangle similar to RST is 12 units long. Find the other side lengths of the triangle.
A B
C
12
x y
Find the value of x that makes corresponding side lengths proportional.
2412
= 30 x
Write proportion.
x = 15
Cross Products Property24x = 12 30
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GUIDED PRACTICE for Examples 1 and 2
Again to find out y
2412
= 33y
Write proportion.
y = 16.5
Cross Products Property24y = 12 33
So x = AC = 15 and y = BC = 16.5
ANSWER