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 Trigonometry
8.1 Geometric Mean
Geometric
Mean
Date
The positive square root of the product between
two numbers
The means are the same in a proportion
8.1 Geometric Mean.notebook
Try examples 1­3 on your practice sheet
January 22, 2014
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
C
A
D
C
D
B
3. In pencil, write the letters of the vertices inside each triangle.
Also, draw the right angle symbol inside ACD.
8.1 Geometric Mean.notebook
January 22, 2014
C
A
D
C
D
B
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
D
D
C
C
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!
B
A
8.1 Geometric Mean.notebook
January 22, 2014
D
D
B
C
C
A
Similarity Statement
~
~
8.1 Geometric Mean.notebook
Try examples 4 and 5 on
your practice sheet
January 22, 2014
8.1 Geometric Mean.notebook
January 22, 2014
D
D
C
C
How could we figure out the length of DC?
B
A
8.1 Geometric Mean.notebook
If CD is the altitude (going from the right angle
to the hypotenuse) of the overall triangle, then
The altitude is the geometric mean of the smaller
lengths of the hypotenuse
h
h
h
C
C
A
D
x
y
y
B
x
D
Big Idea #1
January 22, 2014
8.1 Geometric Mean.notebook
If CD is the altitude (going from the right angle
to the hypotenuse) of the overall triangle, then
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.
a
b
y
x
c
C
b
C
A
y
B
D
x
D
Big Idea #2
January 22, 2014
a
8.1 Geometric Mean.notebook
Try examples 6­9 on your
practice sheet
January 22, 2014
8.1 Geometric Mean.notebook
January 22, 2014
8.1 Geometric Mean.notebook
January 22, 2014
8.1 Geometric Mean.notebook
January 22, 2014