Transcript Chapter 8 Lesson 3 - Mrs.Lemons Geometry

Chapter 8 Lesson 3
Objective: To apply AA, SAS,
and SSS similarity.
Name the postulate or theorem you can use to prove the
triangles congruent.
1.
2.
3.
SSS
SAS
ASA
Name the SIMILARITY postulate or theorem you can use
to prove the triangles congruent.
1.
2.
3.
AA~
SAS~
SSS~
Example 1:
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 2:
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 3: 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 4: 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 435
#10-21, 23, 28-39