Download Chapter 8 Lesson 3(1).

Chapter 8 Lesson 3
Objective: To use AA, SAS and
SSS similarity statements.
Postulate 8-1
Angle-Angle Similarity (AA ~) Postulate
If two angles of one triangle are congruent to two
angles of another triangle, then the triangles are
similar.
∆TRS ~ ∆PLM
Example 1:
Using the AA~ Postulate
Explain why the triangles are similar.
Write a similarity statement.

RSW
VSB because vertical angles are
congruent. R
V because their measures are equal.
∆RSW ~ ∆VSB by the Angle-Angle Similarity Postulate.

Example 2:
Using the AA~ Postulate
MX  AB Explain why the triangles are similar.
Write a similarity statement.
M
K
B
58°
58°
X
A
∆AMX~∆BKX by AA~ Postulate
Theorem 8-1
Side-Angle-Side Similarity (SAS ~) Theorem
If an angle of one triangle is congruent to an angle
of a second triangle, and the sides including the
two angles are proportional, then the triangles are
similar.
Theorem 8-2
Side-Side-Side Similarity (SSS ~) Theorem
If the corresponding sides of two triangles
are proportional, then the triangles are
similar.
Example 3:
Using Similarity Theorems
Explain why the triangles must be similar.
Write a similarity statement.
 QRP  XYZ
because they are right angles.
OR
3
PR
6 3
 and
 
XY
4
ZY
8 4
Therefore, ∆QRP ~ ∆XYZ by the SAS ~ Theorem
Example 4:
Using Similarity Theorems
Explain why the triangles must be similar. Write a similarity
statement.
AC
CB AB 3



EG GF EF
4
∆ABC ~ ∆EFG by SSS~ Theorem
Example 5: Finding Lengths in Similar Triangles
Explain why the triangles are similar.
Write a similarity statement.
Then find DE.
ABC  EBD
Because vertical angles are
congruent.
AB 12 2


EB 18 3
CB 16 2


DB 24 3
ΔABC ~ ΔEBD by the SAS~ Theorem.
CA 2

DE 3
10
2

DE 3
2DE  30
DE  15
Example 6: Finding Lengths in Similar Triangles
Find the value of x in the figure.
6
8

x 12
72  8x
9x
Indirect Measurement is when you use
similar triangles and measurements to
find distances that are difficult to
measure directly.
Example
7:
Indirect Measurement
Geology Ramon places a mirror on the ground 40.5 ft from the
base of a geyser. He walks backwards until he can see the top
of the geyser in the middle of the mirror. At that point,
Ramon's eyes are 6 ft above the ground and he is 7 ft from the
image in the mirror. Use similar triangles to find the height of
the geyser.
∆HTV ~ ∆JSV
HT TV

JS SV
6
7

x 40.5
243  7x
34.7  x
The geyser is about
35 ft. high.
Example 8: Indirect Measurement
In sunlight, a cactus casts a 9-ft shadow. At the same time a
person 6 ft tall casts a 4-ft shadow. Use similar triangles to
find the height of the cactus.
X
6
4
9
9 x

4 6
54  4x
13.5  x
Assignment
Page 437
#1-39(odd)