Download TOPIC 9-3: SIMILAR TRIANGLES

TOPIC 9-3: SIMILAR TRIANGLES
When polygons are similar, two criteria must be met:
1) Corresponding angles are ____________________.
2) Corresponding sides are ___________________________.
However…if you don’t know the measures of all sides and angles, is
there another way to tell?
There are several theorems that allow us to show that triangles are
similar.
AA
Similarity
________________-________________ Similarity
If two angles of one triangle are _____________
to two angles of another triangle, then the
triangles are _________________.
EXAMPLE 1 Can these triangles be proven similar by AA? If so,
write a similarity statement.
G
J
H
F
K
YES
or
NO
∆_________∼
∼∆___________
A second way to show that triangles are similar is:
________________-________________ -_____________ Similarity
In two triangles, if a pair of corresponding angles is
SAS
_______ and the sides including the angle are
Similarity
__________________________, then the triangles
are ______________________.
EXAMPLE 2 Can the two triangles be proven similar by SAS? If
Q
so, write a similarity statement.
L
9
6
M
120°°
N
4
P
YES
or
120°°
R
6
NO
∆___________ ∼∆___________
There is a third way to show that triangles are similar…
________________-________________ -_____________ Similarity
SSS
If all three pairs of corresponding sides of two
triangles are _______________________, then
Similarity
the two triangles are _____________________.
EXAMPLE 3 Are the triangles below similar by SSS? If so, write a
X
similarity statement.
S
T
9
4
3
5
U
W
YES
or
12
15
NO
∆___________ ∼∆___________
V
EXAMPLES Are the two triangles similar? If so, state how and
write a similarity statement.
X
D
4.
5.
5
3
6
E
6
F
G
10
W 80°°
V
6
80°°
Z
Y
H
YES
or
NO
YES
HOW?
or
NO
HOW?
∆________∼
∼∆_________
6. Q
∆________∼
∼∆_________
T
L
7.
10
6
6
18
R
K
3
S
8
5
N
J
U
YES
or
V
24
NO
YES
HOW?
or
NO
HOW?
∆________∼
∼∆_________
8.
M
∆________∼
∼∆_________
R
P
12
3
YES
or
NO
Q
HOW?
4
L
∆________∼
∼∆_________
9
S
EXAMPLES Are the two triangles similar, and if so what is the
common ratio?
9. The measures of the sides of ∆ABC are 4, 5, & 7. The measures
of ∆XYZ are 16, 20, & 28.
10. ∆PQR has sides 3, 5, & 6. ∆STU has sides 2.5, 2, & 3.