Download Geometry Lesson 8-3 Proving Triangles Similar.notebook

Geometry Lesson 8­3 Proving Triangles Similar.notebook
January 24, 2013
Section 8­3 : Proving Triangles Similar
Warm­ Up
Name the postulate or theorem you use to prove the triangles congruent.
3.
2.
1.
Postulate 8­1 : Angle­Angle Similarity (AA ~) Postulate : If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
T
P
R
TRS ~ PLM
S
L
M
1
Geometry Lesson 8­3 Proving Triangles Similar.notebook
January 24, 2013
Example 1) Explain why the triangles are similar. Write a similarity statement.
V
o
45
W
S
45o
B
R
Do we have enough information to write a similarity statement or a similarity ratio?
Theorem 8­1 : Side­Angle­Side 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.
5
10
3
6
2
Geometry Lesson 8­3 Proving Triangles Similar.notebook
January 24, 2013
Theorem 8­2 : Side­Side­Side Similarity (SSS ~) Theorem : If the corresponding sides of two triangles are proportional, then the triangles are similar.
2
3
6
9
4
6
Example 2) Explain why the triangles must be similar. Write a similarity statement.
Z
P
6
Q
3 R
8
X
4
Y
3
Geometry Lesson 8­3 Proving Triangles Similar.notebook
January 24, 2013
You try) Explain why the triangles must be similar. Write a similarity statement.
9
B
A
G
6
6
C
8
8
E
12
F
Example 3) Explain why the triangles are similar. Write a similarity statement. Then find DE.
A
10
12
24
D
C
16 B
18
E
4
Geometry Lesson 8­3 Proving Triangles Similar.notebook
January 24, 2013
You can use similar triangles and measurements to find distances that are difficult to measure directly. This is called indirect measurement.
One method of indirect measurement uses the fact that light reflects off a mirror at the same angle at which it hits the mirror. A second method uses the similar triangles that are formed by certain figures and their shadows. (See next examples.)
Example 4) 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 the 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.
5
Geometry Lesson 8­3 Proving Triangles Similar.notebook
January 24, 2013
You try) In sunlight, a cactus casts a 9­ft shadow. At the same time a person 6 ft tall casts a 4­ft shadow. Use similar triangles to find the height of the cactus.
6