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Geometry Notes
Ratio, Proportion, & Geometric Mean
If a and b are two quantities that are measured in the _________ units, then the ratio
of a to b is written as:
OR
Examples: Simplify the ratios.
1)8 books =
12 books
2) 24 trees=
14 tress
3) 18 balls=
36 balls
4) 48 feet=
36 feet
Answer these questions: The girls soccer team won 10 games and lost 2, the
boys soccer team won 12 games lost 3.
A) What is the ratio of girl’s wins to their losses.
B) What is the ratio of boy’s wins to their losses.
C) What is the ratio of girl’s wins to the total number of games played?
D) What is the ratio of boy’s wins to the total number of games played?
E) Which team had the better record?
Use a number line to find the ratio of the distances.
AB

DE
BC

DE
AC

BD
CF

AB
Find the ratio of width to length of the rectangles. Remember to simplify.
Solving word problems.
1) The measures of the angles in a triangle are in an extended ratio of 3: 4: 5. Find
the measures of the angles.
2) The area of a rectangle is 192 sq. feet. The ratio of the width to the length is 3 :
4. Find the width and the length.
The ratio of the given side lengths of the triangle is given. Solve for the
variable.
3) AB : BC is 2: 5
4) AC:BC:AB is 2 : 1: 2
NAME: ______________________________ DATE: _____________ PERIOD: ______
Geometry Notes- Section 6.1-PAGE 2
Ratio & Proportion
An equation that equates two ratios is called a ___________________.
To solve proportions we use the
Cross Product Property: The product of the means is equal to the product of the
extremes.
a c

b d
where ad = bc
a & d are: ____________
b & c are: ______________
Solve these proportions.
1)
4)
20
m

30 120
2
3

y 3 y
2)
5)
y 2

10 5
3
15

d 2 d
3)
6)
5
x

10 16
5
3

2n  7 n  3
Geometric Mean: The geometric mean of two positive numbers a and b is the positive
number x such that
a
x
=
x
b
To solve:
Examples: Find the geometric mean.
1) 4 and 9
4)
16 and 18
2) 4 and 16
3) 3 and 12
5) 18 and 54