Download Proportional Segments between Parallel Lines

Proportional Segments between
Parallel Lines
Look for the similar Triangles
Parallel Lines and Transversal
Alternate interior angles are congruent if the
lines are parallel
Corresponding angles are congruent if the lines
are parallel
Could use SSI to prove lines parallel
Think of the triangle inside of a triangle and how
you might prove them similar
2
Why are angles 1 and 2 congruent
1
Parallel/Proportionality Conjecture
If a line parallel to one side of a triangle passes
through the other two sides, then it divides the
other two sides proportionally. (This ratio is not
the scale factor between the triangles)
The sides the parallel line intersects creates 2
segments on each side, those 4 segments are
Assume line is parallel to base
proportional
a
b
c
of triangle
d
a c

b d
Converse
If the segments are proportional then the lines
are parallel.
You need to know these conjectures forwards
and backwards
Example
You can use either the triangles
or the proportional segments
a b

c d
ad  bc
Using triangles – ab
cancels
a
b

ac bd
ab  ad  ab  bc
ad  bc
Example
Find AB ___ if EC=9
Extended Parallel/Proportionality
Conjecture
If two or more lines pass through two sides of a
triangle parallel to the third side, then they
divided the two sides proportionally.
This just means you can set up multiple
proportions depending on the segments you are
using on one side of the figure
What proportions
can be set up
a
b
a

b
a

c
b

c
d
e
d
f
e
f
c
d
e
f
Example
Show that sides are divided proportionally, set up similar
triangles and just proportional sides.
Answers to Examples
1. 8
12

16 x
8
9

24 AB
2. 24
x

8 12
Proportional segments x = 24
Here you need to set up similar
triangles AB=27
X= 36
3.
2 3

4 m
m6
2 3

3 n
n  4 .5
Homework
Pg 627 1-13 odd