* Prove certain triangles are similar by using AA~, SSS~, and SAS~ * Use triangle similarity to solve problems.

1. 3.8.4 Triangle Similarity
The student is able to (I can):
• Prove certain triangles are similar by using AA~, SSS~,
and SAS~
• Use triangle similarity to solve problems.

2. Angle-Angle Similarity (AA~)
If two angles of one triangle are
congruent to two angles of another
triangle, then the triangles are similar.
∠M ≅ ∠P
∠A ≅ ∠O
Therefore, ∆MAC ~ ∆POD by AA~
M
A C
P
O
D

3. Side-Side-Side Similarity (SSS~)
If the three sides of one triangle are
proportional to the three corresponding
sides of another triangle, then the
triangles are similar.
W H
Y
N
O
T
= =
WH HY WY
NO OT NT
Therefore, ∆WHY ~ ∆NOT by SSS~
1230
18
16
40
24

4. Side-Angle-Side Similarity (SAS~)
If two sides of one triangle are
proportional to two sides of another
triangle, and the included angles are
congruent, then the triangles are similar.
E
T X
U
L V
=
LU LV
TE TX ∠L ≅ ∠T
Therefore, ∆LUV ~ ∆TEX by SAS~
4
5
2
2.5

5. Example Explain why the triangles are similar and
write a similarity statement.
90 — 56 = 34º
Therefore m∠V = m∠X, thus ∠V ≅ ∠X.
Since m∠U = m∠E = 90º, ∠U ≅ ∠E
Therefore, ∆LUV ~ ∆TEX by AA~
56º
34º
L
U V
T
E
X

6. Example Verify that ∆SAT ~ ∆ORT
A
S
T
R
O
12
15
20
16
∠ATS ≅ ∠RTO (Vertical angles ≅)
12 15
?
16 20
=
240 = 240
Therefore, ∆SAT ~ ∆ORT by SAS~