• 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