January 11, 2012
1) Write your homework in your agenda:
Proportional Parts worksheet
2) Take out your parallel lines worksheet
and leave it on your desk.
3) Take out your Cornell Notes from
yesterday.
4) Take out your angle quiz.
Answers to
Proving Parallel Lines
1)
2)
3)
4)
5)
6)
7)
8)
130o
128o
66o
100o
90o
81o
53o
58o
9) 50o
10) 63o
11) x =
12) x =
13) x =
14) x =
15) x =
16) x =
6
7
-7
6
12
8
What is Two Transversal
Proportionality Theorem?

If three or more parallel lines intersect two
transversals, then they cut off the
transversals proportionally.
B
C
D
A
E
F
G
BC =CD
EF FG
AC= BC
AF EF
AB = AD
AG
AE
CD= FG
AE AB
Two Transversal
Proportionality Theorem
P
In the diagram 1  2 
3, and PQ = 9, QR = 15,
and ST = 11.
What is the length of TU?
S
1
9
11
Q
T
2
15
R
U
3
SOLUTION: Because corresponding angles are
congruent, the lines are parallel and you can use
Two Transversal Proportionality Theorem
PQ = ST
QR
TU
Parallel lines divide
transversals proportionally.
9 = 11
15
TU
Substitute
9 ● TU = 15 ● 11 Cross Product
9TU = 165
Divide each side by 9 and simplify.
55
3
So, the length of TU is 55/3 or 18 1/3.
Two-Transversal
Proportionality Example
Solve for x and y
x
30

15
16 . 5
26
y
26x = 15(30)
x = 225
13

15
26
15y = 16.5(26)
y = 28.6
6
Triangle Proportionality
Theorem
If a line parallel to one
side of a triangle
intersects the other two
sides, then it divides
the two side
proportionally.
Q
T
R
S
If TU ║ QS, then
RT
TQ

RU
US
U
Converse of the Triangle
Proportionality Theorem
If a line intersects two
sides of a triangle and
separates the sides
into corresponding
segments of
proportional lengths,
then the line is
parallel to the third
side.
Q
T
R
U
S
If
RT
TQ

RU
US
, then TU ║ QS.
Example 1
In the diagram AB ║ ED, BD = 8, DC = 4,
and AE = 12. What is the length of EC?
C
BD
4
D
8

DC
AE
EC
8
4
E
12
12

EC
8 x  48
B
A
EC  6
Example 2
Given the diagram, determine whether MN ║GH
LM
G

56

8
MG
21
3
LN
48
3
21
M

NH
56
L
16
8
N
48
16
H

3

1
3
1
MN is not parallel to GH.
Try This…
In the diagram KL ║ MN.
Find the values of the
variables.
J
9
K
L
37.5
7.5
x
13.5
M
y
N
J
9
K
Solution
L
37.5
7.5
x
13.5
M
y
To find the value of x, you can set up a proportion.
9
13.5

37.5  x
x
13.5(37.5 – x) = 9x
506.25 – 13.5x = 9x
506.25 = 22.5 x
22.5 = x
Write the proportion
Cross product
Distributive property
Add 13.5x to each side.
Divide each side by 22.5
N
J
9
K
Solution
L
37.5
7.5
x
13.5
M
y
To find the value of y, you can set up a proportion.
9
13.5  9

7.5
y
9y = 7.5(22.5)
y = 18.75
Write the proportion
Cross product property
Divide each side by 9.
N

Try this one too!
R
9
Q
3
P
S
T
20
PQ
QR
3
9


PT
TS
y
20  y
3(20  y )  9 y
60  3 y  9 y
60  12 y
y5
y
January 13, 2012
1) Grab a Computation Challenge, keep it face
down and put your name on the back
2) Write your homework in your agenda:
Study Guide
3) Take out your worksheet and leave it on
your desk.
Use proportionality Theorems
in Real Life
Building Construction: You
are insulating your attic, as
shown. The vertical 2 x 4
studs are evenly spaced.
Explain why the diagonal
cuts at the tops of the strips
of insulation should have the
same length.
Use proportionality Theorems
in Real Life

Because the studs AD, BE
and CF are each vertical,
you know they are parallel
to each other. Using
Theorem 8.6, you can
conclude that
DE
EF

=
AB
BC
Because the studs are evenly spaced, you know that
DE = EF. So you can conclude that AB = BC, which
means that the diagonal cuts at the tops of the strips
have the same lengths.