# Lesson 8 1 Example 1 Geometric Mean Find the geometric mean between each pair of numbers

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```					Geometry                                                              Chapter 8

Lesson 8-1

Example 1 Geometric Mean
Find the geometric mean between each pair of numbers.
a. 4 and 16
Let x represent the geometric mean.
4   x
=
x 16
Definition of geometric mean
2
x = 64          Cross products
x = 64         Take the positive square root of each side.
x =8           Simplify.

b. 9 and 12
9   x
=
x 12
Definition of geometric mean
2
x     = 108      Cross products
x    = 108      Take the positive square root of each side.
x    =6 3       Simplify.
x    ≈ 10.4     Use a calculator.

Example 2 Altitude and Segments of the Hypotenuse
In ABC, AD = 4 and CD = 12. Find BD.
Let x = BD.
=
BD CD
Theorem 8.2
4   x
=
x 12
AD = 4, CD = 12, and BD = x
2
x    = 48           Cross products
x   = 48           Take the positive square root of each side.
x   =4 3           Simplify.
x   ≈ 6.9          Use a calculator.

Geometry                                                                              Chapter 8

Example 3 Altitude and Length of the Hypotenuse
ARCHITECTURE To find the height of her school building, Mieko held a book near her eye so
that the top and bottom of the building were in line with the edges of the cover. If Meiko's eye level
is 5 feet above the ground and she is standing about 10.25 feet from the building, how tall is the
building? Round to the nearest tenth.
Draw a diagram. Let CD be the altitude
drawn from the right angle of ∆ABC.
=
CD BD
Theorem 8.2
5     10.25
10.25
= BD           AD = 5 and CD = 10.25
5BD = 105.0625       Cross products
BD ≈ 21.0           Divide each side by 5.

The building is 5 + 21.0 or about 26.0 feet high.

Example 4 Hypotenuse and Segment of the Hypotenuse
Find x and y in ABC.
AB and BC are legs of right triangle ABC.
Use Theorem 8.3 to write a proportion
for each leg and the solve.

AC AB                                               AC BC
=
Theorem 8.3                           =
BC CD
Theorem 8.3
10 y                                                10 x
y
=4            AC = 10, AB = y, AD = 4
x
=6         AC = 10, BC = x, CD = 6
2                                                  2
y     = 40       Cross products                     x    = 60     Cross products
y    = 40       Take the square root.               x   = 60     Take the square root.
y    = 2 10     Simplify.                           x   = 2 15   Simplify.
y    ≈ 6.3      Use a calculator.                   x   ≈ 7.7    Use a calculator.

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