• Answer questions over homework
• 6.6: Using Proportionality Theorems
• Homework: ws 6.6
• Next Class: Geometric mean
Find the height of the tree, to the
hrearest thousandth given:
75 in.
35 in. 187 in.
400.714 in
6.6: Using Proportionality
Theorems
Chapter 6
Objectives:
• Develop, apply, and justify triangle similarity
relationships.
Think about it… When you get pictures developed, how does
the picture make you look only a fraction of
what your actual size is?
• If a line _________ to one side of a
triangle ____________ the other two
sides, then it __________ the two sides
_________________.
• The converse is
also true.
Triangle Proportionality Theorem
parallel
intersects
divides
proportionally
Triangle Proportionality Theorem
Example
In the diagram, QS || UT, RS = 4, ST = 6, and
QU = 9. What is the length of RQ?
SOLUTION
Substitute
Multiply and simplify
Triangle
Proportionality Thm =
Try 1-4 on
6.6 Proportionality Theorems
More Theorems • If three parallel lines intersect two
tranversals, then they divide the transversals
______________ .
proportionally
Example
Corresponding angles are congruent, so
FE, GD, and HC are parallel. So, we
can use the theorem we just learned!
Try 15 and 16 on
6.6 Proportionality Theorems
Altitudes, Medians, and Angle
Bisectors Investigation
On an unlined sheet of paper, draw a
triangle using your ruler. I recommend
that your triangle is drawn with easy
numbers, for example 5 cm, 6 cm, and 7 cm.
Altitudes, Medians, and Angle
Bisectors Investigation
Now draw a triangle that is similar to this.
State your scale factor. I will use a scale
factor of 2.
Altitudes, Medians, and Angle
Bisectors Investigation
Draw in the altitudes of the triangles.
Using the ruler determine how the two
altitudes compare.
Altitudes, Medians, and Angle
Bisectors Investigation
Now, draw in your medians and angle
bisectors. How do they compare?
ANGLE BISECTORS
Altitudes, Medians, and Angle
Bisectors Conclusion
CONCLUSION: If two triangles are similar,
then the corresponding altitudes, medians,
and angle bisectors are proportional to
corresponding sides.
Altitudes, Medians, and Angle
Bisectors Example Find x:
Try 17 on
6.6 Proportionality Theorems
Angle Bisector Theorem
• An angle bisector in a triangle separates the
opposite side into segments that have the
same ________ as the other two sides. ratio
14
10
35
x
14 10
35 x
X = 25
Example
15-x
( )
How would you define QR? “in terms of x”
Try 8-10 on
6.6 Proportionality Theorems
Practice
• finish class worksheet
• Get Ws 6.6 from me, complete it