Star Wars Revenge of the Sith
Proving Triangles Similar by AA, SSS, and SAS
Name____________
K
Y
L
Z
Angle-Angle (AA) Similarity Postulate –
X
J
Side-Side-Side (SSS) Similarity Theorem –
R
A
S
B
T
C
Side-Angle-Side (SAS) Similarity Theorem –
X
M
P
N
Y
Z
Example 1
Determine whether the triangles are similar. If they are, write a similarity statement.
D H
C
26
64
E
K
G
Examples
Show that the two triangles are similar. Then write a similarity statement.
2. ABE and ACD
3. CDF and DEF
D
A
52
E
B
D
C
C
Example 4
Is either DEF or GHJ similar to ABC?
B
12
D
8
F
H
F
10
12
6
8
9
E
A
16
58
32
52
C
J
16
G
E
Example 5
A flagpole casts a shadow that is 50 feet long. At the same time, a woman standing nearby who is five
feet four inches tall casts a shadow that is 40 inches long. How tall is the flagpole to the nearest foot?
Example 6
Find the value of x that makes ABC ~ DEF.
E
B
x- 1
4
18
12
A
C
8
D
F
3(x + 1)
G
Example 7
Complete the following proof.
82
mK  48
mJ  50
mG  82
GIVEN:
GKF
PROVE:
K
48
F
50
J
GHJ
Statements
Reasons
1.
1. Given
2. mJ  50
2.
3.
3. Given mG  82
3. mG  mK  mF  180
3.
4.
4. Substitution property
5.
5. Combine like terms
6. mF  50
6.
7. mF  mJ
7.
8.
8. Definition of congruent angles
9.
9. Reflexive property
10.
10. AA
H