7.3 - Similar Triangles
Getting Started
1.) If the ratio of guys to girls in Coach Holman's class is
3:2, and there are 348 students in the entire freshman
class. Estimate the number of girls in the freshman class.
2.) If a baseball player gets 9 hits in 22 games, how many
hits does he get per game?
3.) A model airplane has a scale factor of 2:255 of the
actual plane. If the wingspan of the model plane is 6 inches,
what is the wingspan of the actual plane (in feet)?
7.3 - Proving Triangles are Similar
Objectives
1.) Use Similarity Theorems (AA, SAS, SSS)
2.) Apply similar triangles for indirect measure.
3.) Write Proofs for Similar Triangles
Angle-Angle (AA) Similarity
If two angles of one triangle are congruent to
two angles of another triangle, then the
triangles are similar.
Q
T
))
R
)
)
))
S
V
W
Side - Side - Side (SSS) Similarity
Theorem
IF
AB BC = CA
=
XY YZ ZX
B
Then
ABC ~
XYZ
A
C
X
Y
Z
Side - Angle - Side (SAS) Similarity
Theorem
B
4
8
Y
)
)
Draw:
A
IF
A X and AB = AC
XY XZ
Then
5
ABC ~
X
C
XYZ
2.5
Z
Is WYZ ~ WXT? Explain your reasoning using as many key
vocabulary terms as you can.
Z
>>
Y
>>
)
X
W
T
12
~
A
6
A
B
Long
Long
6
B
x
9
Short
Short
Mid
Mid
4
R
F
S
X
H
FHG ~ RXS
G
FH
=
XS
=
FG
S
4
P
12
R
Is
SPQ ~
5
Q
SRT
15
T
What Similarity Theorem did you use?
What else do you know about the diagram? Specifically about the
line segments?
Indirect Measure - Using SIMILAR triangles and proportions to find
lengths, heights and distances of
objects.
Use what you can measure
to find what you can't.
6.2
25.9
3.7
Using Similar Triangles in Real Life
- Using a Mirror
h
6
8
840
Measure Impassable Terrain
63
X
Ninja
Fish w/
nunchucks
12
9
Pre-AP Geometry
7.3 - Similar Triangles
Name: ___________________________
Class Period: ______
Use the diagram to determine whether the triangles are congruent. If so, write a similarity statement,
and identify the Similarity Theorem that you used to make your determination. If not, identify what
information would be sufficient to prove the triangles similar.
1.)
2.)
9
||
12
8
|
)
__
9
6
)
||
12
3.)
4.)
60o
15
o
10 70
70o
14
21
30o
Assume that each pair of triangles is similar. Find each measure.
5.)
6.)
A
x+1
J
15
)
)
B
12
K
8
^
6
^
x+5
C
x-1
x+7
7.) A 445' radio tower sits atop a 137' hill, and has a radial transmission distance of 309 miles.
7a.) If a tower with the same capabilities is built 550 miles away NOT on top of a hill, will the two radio
signals overlap? Sketch the situation, and explain.
7b.) What is ratio of tower height coverage area?
7c.) The minimum height of a tower in order to get any useable coverage is 350'. How many 350' towers,
built on the same latitudinal lines would it take in order to have 1300 miles of uninterrupted radio
coverage?
7d.) How many 500' towers built on the same latitudinal line would it take to get 1300 miles of
uninterrupted radio coverage?
7e.) If the cost to build a tower is $200/vertical foot, and you needed to cover 1300 linear miles, is it
more cost efficient to build 350' towers or 500' towers? Diagram and label each situation, and explain
your reasoning. Use the rest of the bottom of this page... Unless you're scared.