Geometry
Name_________________________
Geometry - Warm Up
Solve the proportion.
16 12  x
1.

32
x
1
7

x  1 2x  8
2.
Find the value of x.
GK JK
3.

GH FH
G
3
J
K
9
F
5
H
x
4. The polygons shown are similar. Find the value of each variable.
10
5
10
z
x
15
y
35
5. In sunlight, a baby giraffe casts a shadow of 11 ft. At the same time a person 5 feet 5 inches tall
casts a shadow of 3 feet. Use similar triangles to find the height of the giraffe.
A
6. Complete the following proof.
EB llDC
GIVEN:
PROVE:
AEB
E
ADC
D
Statements
Reasons
1.
1. Given
2.
2. Reflexive property
3. AEB  ADC
3.
4. AEB
4.
ADC
STOP HERE
B
C
Today:
We will understand how to use Proportionality Theorems…….
And you will be able to find lengths in similar triangles.
Using Proportionality Theorems
Triangle Proportionality Theorem –
Q
T
RT RU

.
If TU QS, then
TQ US
R
U
S
Converse of the Triangle Proportionality Theorem –
Q
T
RT RU

, then TU QS.
If
TQ US
R
U
S
Examples
1. In the diagram, QS UT, RS = 4, ST = 6, and QU = 9. What is the length of RQ ?
9
U
Q
R
4
S
6
T
2. Find the length of YZ.
V
W
35
44
X
36
Y
Z
Theorem –
UW VX

WY XZ
U
W
Y
V
X
Z
Theorem –
A
AD CA

DB CB
D
C
B
Examples
3. In the diagram, QPR  RPS. Use the given side lengths to find the length of RS.
Q
7
R
P
15
x
13
S
Find the length of AB.
4.
5.
C
4
B
16
D
4 2
A
4
15
B
A
18
6.
7.
24
16
y
x
36
16
10
28