Identify similar triangles Use properties of similar triangles to solve problems

1. Similar Triangle Properties
The student is able to (I can):
• Use properties of similar triangles to find segment lengths.
• 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, ΔMAC ~ ΔPOD 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, ΔWHY ~ ΔNOT 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, ΔLUV ~ ΔTEX by SAS~
4
5
2
2.5

5. Example:
Explain why the triangles are similar and write a similarity
statement.
56°
34°
L
U V
T
E
X

6. Example:
Explain why the triangles are similar and write a similarity
statement.
90 – 56 = 34°
Therefore m∠V = m∠X, thus ∠V ≅ ∠X.
Since m∠U = m∠E = 90°, ∠U ≅ ∠E
Therefore, ΔLUV ~ ΔTEX by AA~
56°
34°
L
U V
T
E
X

7. Example:
Verify that ΔSAT ~ ΔORT
S
T
R
O
12
15
20
16

8. Example:
Verify that ΔSAT ~ ΔORT
A
S
T
R
O
12
15
20
16
∠ATS ≅ ∠RTO (Vertical angles ≅)
12 15
?
16 20
=
240 = 240
Therefore, ΔSAT ~ ΔORT by SAS~