Geometry
Notes
Name_________________________
Proving Triangles Similar by AA, SSS, and SAS
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. If similar triangles are being formed, 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
12
A
8
C
D
Example 7
Tell what method you would use to show that the triangles are similar.
Then write a similarity statement.
18
3(x + 1)
F