8.1 Geometric Mean.notebook January 22, 2014

"Do Now"

Solve each proportion.

Ms. Stalvey ran a 5K over the weekend through downtown

Greenville in 23:55!

8.1 Geometric Mean.notebook January 22, 2014

Unit 9: Right Triangles and Trigonometry8.1 Geometric Mean Date

GeometricMean

The positive square root of the product between two numbers

The means are the same in a proportion

8.1 Geometric Mean.notebook January 22, 2014

Try examples 1­3 on your practice sheet

8.1 Geometric Mean.notebook January 22, 2014

1.  Cut out       ABC.

(Cut around the letters of the vertices.)

8.1 Geometric Mean.notebook January 22, 2014

2.  On the 2nd copy, outline the two inside triangles.

Use green for       ACD and blue for      CBD.

8.1 Geometric Mean.notebook January 22, 2014

3.  In pencil, write the letters of the vertices inside each triangle.

Also, draw the right angle symbol inside       ACD.

A

C C

BDD

8.1 Geometric Mean.notebook January 22, 2014

C

BD

A

C

D

4.  Cut out      ACD and      CBD.

Write the letters of the vertices on the back of each triangle.

8.1 Geometric Mean.notebook January 22, 2014

C B

D

A C

D

5.  Orient the 3 triangles the same way.

What do you notice?

3 similar triangles are formed by the altitude DC in the overall triangle!

8.1 Geometric Mean.notebook January 22, 2014

C B

D

A C

D

Similarity Statement

~ ~

8.1 Geometric Mean.notebook January 22, 2014

Try examples 4 and 5 on your practice sheet

8.1 Geometric Mean.notebook January 22, 2014

C B

D

A C

D

How could we figure out the length of DC?

8.1 Geometric Mean.notebook January 22, 2014

Big Idea #1

The altitude is the geometric mean of the smaller lengths of the hypotenuse

C B

D

A C

D

x y

h

x hh y

If CD is the altitude (going from the right angle to the hypotenuse) of the overall triangle, then

8.1 Geometric Mean.notebook January 22, 2014

Big Idea #2

The leg of the overall right triangle is the geometric mean between the overall hypotenuse and the portion of the hypotenuse adjacent to that leg.

C B

D

A C

D

x y

x y

If CD is the altitude (going from the right angle to the hypotenuse) of the overall triangle, then

c

b a

b a

8.1 Geometric Mean.notebook January 22, 2014

Try examples 6­9 on your practice sheet

8.1 Geometric Mean.notebook January 22, 2014

8.1 Geometric Mean.notebook January 22, 2014

8.1 Geometric Mean.notebook January 22, 2014