9 6 proportional parts and parallel lines
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Proportional Parts and Parallel Lines Proportional Parts and Parallel Lines You will learn to identify and use the relationships betwee parallel lines and proportional parts. Nothing New!
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Transcript of 9 6 proportional parts and parallel lines
Proportional Parts and Parallel Lines Proportional Parts and Parallel Lines
You will learn to identify and use the relationships betweenparallel lines and proportional parts.
Nothing New!
Proportional Parts and Parallel Lines Proportional Parts and Parallel Lines
On your given paper, draw two (transversals) lines intersecting the parallel lines.
C
D
E
F
A
BLabel the intersections of the transversals and the parallel lines,as shown here.
Measure AB, BC, DE, and EF.
,Calculate each set of ratios:BC
AB
EF
DE
AC
AB
DF
DE,
Do the parallel lines divide the transversals proportionally? Yes
Proportional Parts and Parallel Lines Proportional Parts and Parallel Lines
Theorem 9-8
If three or more parallel lines intersect two transversals,the lines divide the transversals proportionally.
l
m
n
B
A
C F
E
D
If l || m || n
AC
BC
DF
EF=Then
BC
AB
EF
DE= ,
AC
AB
DF
DE= and,
Proportional Parts and Parallel Lines Proportional Parts and Parallel Lines
a
b
c
H
G
J W
V
U
18
12
x
15
Find the value of x.
HJ
GH
VW
UV=
18
12
x
15=
12x = 18(15)
12x = 270
x = 222
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Proportional Parts and Parallel Lines Proportional Parts and Parallel Lines
Theorem 9-9
If three or more parallel lines cut off congruent segments onone transversal, then they cut off congruent segments onevery transversal.
l
m
n
B
A
C F
E
D
If l || m || n and
Then
AB BC,
DE EF.
Proportional Parts and Parallel Lines Proportional Parts and Parallel Lines
(x +3)
10
(2x – 2)
10
Find the value of x.
F
(x + 3) = (2x – 2)
x + 3 = 2x – 2
5 = x
Theorem 9 - 9
8 8
ED
C
B
A
DE EF
Since AB BC,
Proportional Parts and Parallel Lines Proportional Parts and Parallel Lines
