Download topic 2-3: identifying similar triangles

TOPIC 9-4: 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
If two angles of one triangle are _____________
to two angles of another triangle, then the
Similarity
triangles are _________________.
EXAMPLE 1 Can these triangles be proven similar by AA? If so,
write a similarity statement.
G
A
a)
b)
J
H
C
E
F
K
B
YES
or
NO
D
____________________
YES
or
NO
___________________
You can use AA Similarity to find missing measurements in triangles.
EXAMPLE 2 Given AB  CD, AB = 4, AE = 3x + 1, CD = 8, and
ED = x + 12, find AE and DE.
A
C
E
B
D
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 3 Can the two triangles be proven similar by SAS? If
so, write a similarity statement.
Q
L
9
6
M
4
120
N
P
YES
or
6
NO
___________ ___________
120
R
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 4 Are the triangles below similar by SSS? If so, write a
similarity statement.
X
S
T
9
4
3
U
5
12
W
YES
or
V
15
NO
___________ ___________
EXAMPLE 5 Are the two triangles similar? If so, state how and
write a similarity statement.
X
5.
6.
7.
L
E
W 80
V
K
80
YES
Y
or
NO
HOW?
_________________
6
6
F
G
M
3
Z
5
3
10
6
D
5
10
6
N
J
H
YES
or
NO
HOW?
_________________
YES
or
NO
HOW?
_________________
EXAMPLE 6 Solve for ‘x’ and for ‘y’.
A
x
B
8
y
E
3
D
3
4
C
EXAMPLE 7 Are the two triangles similar, and if so what is the
common ratio?
a. The measures of the sides of ABC are 4, 5, & 7. The measures
of XYZ are 16, 20, & 28.
b. PQR has sides 3, 5, & 6. STU has sides 2.5, 2, & 3.