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.
â M â â P
â A â â O
Therefore, ÎMAC ~ ÎPOD 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, ÎWHY ~ ÎNOT 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 â L â â T
Therefore, ÎLUV ~ ÎTEX 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 â 56 = 34°
Therefore mâ V = mâ X, thus â V â â X.
Since mâ U = mâ E = 90°, â U â â E
Therefore, ÎLUV ~ ÎTEX by AA~
56°
34°
L
U V
T
E
X