21
8-3 Proving Triangles Similar Advanced Geometry
8-3
Proving Triangles
Similar
Advanced Geometry
Warm Up
Solve the proportion.
1) 2)
3) What’s the difference between similar and
congruent?
16
123
x 8
75
7
26
xx
Angle – Angle
(AA )
If two angles of one triangle are congruent to
two angles of another triangle, then they are
similar
A
BC
D
E
FSimilarity Statement:
ABC DEF
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
3cm9cm
4cm 12cmA
B
C
D
E
FSimilarity Statement:
ABC DEF
Side Side Side
(SSS )
If the corresponding sides of two triangles are
proportional, then the triangles are similar
5 in 15 in
6 in 18 in
8 in24 inA
B
C
D
E
F
Similarity Statement:ABC DEF
5
15 =
6
18 =
8
24
Ex1:
Explain why they are similar
58 58
E
A
B
DC
24 in
12 in36 in
18 in
I
J
F
G
H
Ex1:
Explain why they are similar
58 58
E
A
B
DC
24 in
12 in36 in
18 in
I
J
F
G
H
SASAA
12
24 =
18
35
Ex2:
Write a Similarity Statement
58 58
E
A
B
DC
24 in
12 in36 in
18 in
I
J
F
G
H
Ex2:
Write a Similarity Statement
58 58
E
A
B
DC
24 in
12 in36 in
18 in
I
J
F
G
H
ABD CEDJGF IHF
Ex 3: Explain why they are
similar, find x, y
y
x
15 cm
17 cm
8 cm
12 cm
Ex 3: Explain why they are
similar, find x, y
y
x
15 cm
17 cm
8 cm
12 cm
AA
Ex 3: Explain why they are
similar, find x, y
y
x
15 cm
17 cm
8 cm
12 cm
AA
12
20 =
17
x
Ex 3: Explain why they are
similar, find x, y
y
x
15 cm
17 cm
8 cm
12 cm
AA
12
20 =
17
x
x = 281
3
Ex 3: Explain why they are
similar, find x, y
y
x
15 cm
17 cm
8 cm
12 cm
AA
12
20 =
17
x
x = 281
3
12
20 =
15
s
Ex 3: Explain why they are
similar, find x, y
y
x
15 cm
17 cm
8 cm
12 cm
AA
12
20 =
17
x
x = 281
3
12
20 =
15
s
s = 25
Ex 3: Explain why they are
similar, find x, y
y
x
15 cm
17 cm
8 cm
12 cm
AA
12
20 =
17
x
x = 281
3
12
20 =
15
s
s = 25
y = 10
Ex 4: Using the Similarity
Theorems
What theorem or postulate
state that the two triangles
similar?
450
450
V
S
R
W
BVR Given
VSBWSR Angles Vertical
VSBRWS ~ Postulate ~AA
1.
2.
3.
1.
2.
3.
Ex 5: Using Similarity Theorems
Write a similarity statement for the two
triangles. G
E
A B
FC
98
6
8
6
12
Triangle Large
Triangle Small
8
6
8
6
12
9
4
3
4
3
4
3
ratio. 4:3 a have sides all because ~ EFGABC
Ex 6: Finding Lengths in Similar
Triangles
Find the value of x in the figure.
6
8
x
12
Triangle Large
Triangle Small
x
6
12
8
12
86
x
x8)12(6
x872
9x
Stations
Problems #1 – 12: State how the triangles
are similar in the 1st box and then write the
similarity statement in the 2nd box
Problems #13 – 16: Write the proportion in
the 1st box, solve for x, and write the solution
in the 2nd box.
Go to your assigned station, complete it, and
then rotate to complete the others.
Homework
p. 341 #1, 3 – 5, 7, 11, 12, 16, 19, 22
