Download 8-3 Proving Triangles Similar

8-3
Proving Triangles
Similar
Advanced Geometry
Angle – Angle 
(AA  )

If two angles of one triangle are congruent to
two angles of another triangle, then they are
similar
D
A
C
B
Similarity Statement:
ABC  DEF
F
E
Side Angle Side
(SAS  )


If an angle of one triangle is congruent to an
angle of another triangle and the sides
including the two angles are proportional,
then the triangles are similar
A
3cm
D
4cm
B
9cm
12cm
E
C
F
Similarity Statement:
ABC  DEF
Side Side Side
(SSS  )

If the corresponding sides of two triangles are
proportional, then the triangles are similar
B
6 in
A

E
15 in
5 in
18 in
C
F
8 in
5
6
8
=
=
15 18 24
24 in
D
Similarity Statement:
ABC  DEF
Ex1:
Explain why they are similar
I
B
G
36 in
F
E
24 in
A
J
58
58
D
12 in
C
18 in H
Ex1:
Explain why they are similar
I
B
G
36 in
12 in
F
E
18 in H
24 in
A
J
58
58
D
AA
C
12 18
=
24 35
SAS
Ex2:
Write a Similarity Statement
I
B
G
36 in
F
E
24 in
A
J
58
58
D
12 in
C
18 in H
Ex2:
Write a Similarity Statement
I
B
G
36 in
12 in
F
E
18 in H
24 in
A
58
C
D
ABD 
J
58
CED
JGF 
IHF
Ex 3: Explain why they are
similar, find x, y
15 cm
12 cm
17 cm
y
8 cm
x
Ex 3: Explain why they are
similar, find x, y
AA
15 cm
12 cm
17 cm
y
8 cm
x
Ex 3: Explain why they are
similar, find x, y
AA
12 17
=
20
x
15 cm
12 cm
17 cm
y
8 cm
x
Ex 3: Explain why they are
similar, find x, y
AA
12 17
=
20
x
1
x = 28
3
15 cm
12 cm
17 cm
y
8 cm
x
Ex 3: Explain why they are
similar, find x, y
AA
12 17
=
20
x
1
x = 28
3
15 cm
12 cm
12 15
=
20
s
17 cm
y
8 cm
x
Ex 3: Explain why they are
similar, find x, y
AA
12 17
=
20
x
1
x = 28
3
15 cm
12 cm
12 15
=
20
s
17 cm
y
8 cm
x
s = 25
Ex 3: Explain why they are
similar, find x, y
AA
12 17
=
20
x
1
x = 28
3
15 cm
12 cm
12 15
=
20
s
17 cm
y
8 cm
x
s = 25
y = 10
Ex 4: Using the Similarity
Theorems
What theorem or postulate
state that the two triangles
similar?
1.
R  V
2. WSR
3.
1.
Given
 VSB
2.
Vertical Angles
RWS ~ VSB
3.
AA ~ Postulate
V
W
S
450
450
R
B
Ex 5: Using Similarity Theorems

Write a similarity statement for the two
triangles.
9
A
6
6 9
Small Triangle
 

8
8 12
Large Triangle
B
6
6
C
E
G
8
8
12
3 3 3
 
4 4 4
ABC ~ EFG because all sides have a 3 : 4 ratio.
F
Ex 6: Finding Lengths in Similar
Triangles

Find the value of x in the figure.
6 8
Small Triangle


x 12
Large Triangle
6
8
6 8

x 12
6(12)  8 x
72  8x
x 9
12
x
Homework


p. 336 #3 - 5, 7-10, 17
p. 341 #3 – 5, 12, 16