Download Postulate 22: Angle-Angle (AA) Similarity Postulate If two angles of

Geometry
Notes 6.4 and 6.5
Name_________________________
Proving Triangles Similar by AA, SSS, and SAS
Postulate 22: Angle-Angle (AA) Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle,
then the two triangles are similar.
K
Y
L
Z
X
J
Theorem 6.2: Side-Side-Side (SSS) Similarity Theorem
If the corresponding side lengths of two triangles are proportional, then the
triangles are similar.
R
A
S
B
Example: Is either
or
B
similar to
12
D
8
?
H
F
10
12
6
C
8
9
E
A
16
C
J
Example: Find the value of x that makes
3( x 1)
G
16
.
T
Theorem 6.3: Side-Angle-Side (SAS) Similarity Theorem
If an angle of one triangle is congruent to an angle of a second triangle and the
lengths of the sides including these angles are proportional, then the triangles
are similar.
X
M
P
N
Y
Z
Examples
1. Determine whether the triangles are similar. If they are, write a similarity statement.
D H
C
26
64
E
K
G
Show that the two triangles are similar. Then write a similarity statement.
2. ABE and ACD
3. CDF and DEF
D
A
E
52
B
D
58
32
52
C
C
F
E
4. 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?
5. Tell what method you would use to show that the triangles are similar.
D
A
15
18
C
B
9
30
E
Example: Determine if the triangles are similar. If they are, write a
similarity statement and justify why they are similar.