Download Section 4-2 - winegardnermathclass

Section 8-1
Pages 432-438
Geometric Mean
After today’s lesson you should be able to:
- Find the geometric mean between two numbers.
- Solve problems involving relationships between parts of a
right triangle and the altitude hypotenuse.
Geometric Mean- for two positive numbers a and b, the geometric
mean is the positive number x where the proportion a : x = x : b.
This proportion can be written using fractions as a/x = x/b or with
cross products x2 = ab or x = √ab.
Ex. 1: Find the geometric mean between 2√2 and 3√2.
5
5
Ex. 2: The geometric mean is √24. Find b if a = 2.
Theorem 8.1:
ΔXYZ ~ ΔXWY
Z
W
X
Y
Theorem 8.2:
Z
YW is the geometric mean of XW and ZW.
W
X
Y
Theorem 8.3:
XZ = XY and XZ = YZ
XY XW
YZ WZ
Z
W
X
Y
Ex. 3: Find x, y, and z to the nearest tenth.
y
x
z
1
8
Ex. 4: Find x, y, and z to the nearest tenth.
z
x
y
2
6