Transcript 6.6: Use Proportionality Theorems

Warm-Up 1
In the diagram, DE is
parallel to AC.
Name a pair of similar
triangles and explain
why they are similar.
B
D
E
C
A
B
B
DBE ~ ABC
AA (corresponding
angles are congruent
when parallel lines are
cut by a transversal)
D
E
A
C
Warm-Up 2
In the diagram, notice
that AC divides the
sides of the PBD
proportionally. In
PA PC
other words, AB  CD .
What relationship
exists between AC
and BD? Are they
parallel?
B
6
A
12
P
18
C
9
D
Warm-Up 3
In the diagram, lines
AD, BE, and CF are
parallel. What
relationship exists
between AB, DE,
BC, and EF?
D
A
E
B
F
C
Warm-Up 4
Ray AD is an angle
bisector. Notice
that it divides the
third side of the
triangle into two
parts. Are those
parts congruent?
Or is there some
other relationship
between them?
B
D
A
C
6.6: Use Proportionality Theorems
Objectives:
1. To discover, present, and use various
theorems involving proportions with
parallel lines and triangles
Proportionality Theorems!
Triangle
Proportionality
Theorem
If a line parallel to one
side of a triangle
intersects the other
two sides, then it
divides the two
sides proportionally.
Example 1
Find the length of YZ.
28.64
Proportionality Theorems!
Converse of the
Triangle
Proportionality
Theorem
If a line divides two
sides of a triangle
proportionally, then
it is parallel to the
third side.
Example 3
Determine whether PS || QR.
Yes
Example 4
Find the value of
x so that
BC || ED.
x=30
Proportionality Theorems!
If three parallel lines
intersect two
transversals, then
they divide the
transversals
proportionally.
Click here to
investigate these
realtionships
Example 5
Find the length of AB.
Example 6
Find the value of x.
12.5
Proportionality Theorems!
Angle Bisector
Proportionality
Theorem
If a ray bisects an angle of
a triangle, then it divides
the opposite side into
segments whose
lengths are proportional
to the other two sides.
Example 7
Find the value of x.
x=10
Example 8
Find the value of x.
9.75