Download Proportional Segments between Parallel Lines

Proportional Segments between
Parallel Lines
Parallel Lines and Transversal
Alternate interior angles are congruent if the
lines are parallel
Corresponding angles are congruent if the lines
are parallel
Given the picture list all corresponding angles,
list all Alternate interior angles (assume lines are
1
2
parallel)
3
5
8
4
6
7
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)
Conversely, if a line cuts two sides of a triangle
proportionally, then it is parallel to the third
Assume line is parallel to base
side.
a
b
of triangle
c
d
a c

b d
Example
Example
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.
a
b
c
d
e
f
a d

b e
a d

c f
Example
Show that sides are divided proportionally, set up similar
triangles and just proportional sides.
Homework
Pg 605 1-11 odd
Pg 627 1-9 odd