Transcript Geometry Section 6.1

Geometry
Section 6.1
Ratios, Proportions, and the
Geometric Mean
Ratio
The ratio of a to b is
Also written as a:b
a
b
Usually expressed in simplest form
2 ratios that have the same simplified forms are
called equivalent ratios
Examples
Simplify the ratio
24 yards to 3 yards
150 cm : 6 m
The perimeter of a room is 48 feet and the
ratio of its length to its width is 7 : 5. find
the length and width of the room.
Using extended ratios
A triangle’s angle measures are in the
extended ratio of 1 : 3 : 5. find the
measures of the angles.
Proportions
An equation that states that the two
ratios are equal.
Cross product property.
In a proportion the product of the
extremes equals the product of the
means.
Examples
Solve the Proportion
2 5

x 8
1
4

x  3 3x
y 3 y

7
14
Example
As part of a science project, you need
to estimate the number of blue
spruce trees in a 50 acre forest. You
count 36 trees in 3 acres and notice
that the trees seem to be evenly
distributed. Estimate the total
number of blue spruce trees in the
forest.
Geometric Mean
The geometric mean of two positive numbers a and
b is the positive number x that satisfies a  x
x b
so x 2  ab and x  ab
Examples
Find the geometric mean of the two
numbers
12 and 27
18 and 54
16 and 18
Assignment
Section 6.1
Page 360
Problems #4 – 44 even, 50