1. EXAMPLE 1
Use the SSS Similarity Theorem
Is either DEF or GHJ similar to ABC?
SOLUTION
Compare ABC and DEF by finding ratios of corresponding side lengths.
Shortest sides AB DE 4 3 8 6 =

2. EXAMPLE 1
Use the SSS Similarity Theorem
Longest sides CA FD 4 3 16 12 =
Remaining sides BC EF 4 3 12 9 =
All of the ratios are equal, so ABC ~ DEF.
ANSWER
Compare ABC and GHJ by finding ratios of corresponding side lengths.
Shortest sides AB GH 8 = 1

3. EXAMPLE 1
Use the SSS Similarity Theorem
Longest sides CA JG 16 = 1
Remaining sides BC HJ 6 5 12 10 =
The ratios are not all equal, so ABC and GHJ are not similar.
ANSWER

4. Use the SSS Similarity Theorem
EXAMPLE 2
Use the SSS Similarity Theorem
ALGEBRA
Find the value of x that makes ABC ~ DEF.
SOLUTION
STEP 1
Find the value of x that makes corresponding side lengths proportional. 4 12 =
x –1 18
Write proportion.

5. Use the SSS Similarity Theorem
EXAMPLE 2
Use the SSS Similarity Theorem
= 12(x – 1)
Cross Products Property
72 = 12x – 12
Simplify.
7 = x
Solve for x.
Check that the side lengths are proportional when x = 7.
STEP 2
BC = x – 1 = 6 AB DE BC EF = ? 6 18 4 12 =

6. Use the SSS Similarity Theorem
EXAMPLE 2
Use the SSS Similarity Theorem
DF = 3(x + 1) = 24 AB DE AC DF = ? 8 24 4 12 =
When x = 7, the triangles are similar by the SSS Similarity Theorem.
ANSWER

7. GUIDED PRACTICE
for Examples 1 and 2
1. Which of the three triangles are similar? Write a similarity statement.

8. GUIDED PRACTICE
for Examples 1 and 2
SOLUTION
Compare MLN and RST by finding ratios of corresponding side lengths. LM RS 5 6 20 24 =
Shortest sides ST LN 33 24 =
Longest sides LN RT 36 30 = 13 15
Remaining sides
The ratios are not all equal, so LMN and RST are not similar.

9. GUIDED PRACTICE
for Examples 1 and 2
Compare LMN and ZYX by finding ratios of corresponding side lengths. LM YZ 2 3 20 30 =
Shortest sides 2 3 = LN XZ 26 39
Longest sides MN XZ 24 36 = 2 3
Remaining sides
All of the ratios are equal, so MLN ~ ZYX.
ANSWER

10. 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. 24 12 = 30 x
Write proportion.
24x =
Cross Products Property
x = 15

11. GUIDED PRACTICE for Examples 1 and 2 Again to find out y 24 33 = 12 y
Write proportion.
24y =
Cross Products Property
y = 16.5
So x = AC = 15 and y = BC = 16.5
ANSWER