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Transcript
```Section 6.1 Ratios, Proportions, & the Geometric Mean
Goal  Solve problems by writing and solving proportions.
Ratio of a to b
A comparison of two numbers
a to b or
a:b
or
a
b
The ratio of triangle ABC to triangle DEF
would be written as:
Example 1: Simplify the ratio.
a. 64 m: 6 m
b.
4 ft
24in
Example 2: In the diagram, AB:BC is 4:1 and AC = 30. Find AB and BC.
A
B
C
Extended Ratio: Ratios that go beyond the comparison of 2 quantities.
Example 3: The measures of the interior angles of CDE are of the extended ratio of
2:3:4. Find the measures of all 3 angles.
Checkpoint
1. A triangle’s angle measures are in the extended ratio of 1:4:5. Find the measures of the
angles.
Example 4: The perimeter of a room is 48 feet. The ratio of the length to the width is 7:5. Find
the length and width of the room.
Example 5: You are going to paint a rectangular wall. The perimeter of the wall is 484 feet.
The ratio of the length to the width is 9:2. Find the area of the wall.
Section 6.1 Ratios, Proportions, & the Geometric Mean
A PROPERTY OF PROPORTIONS
Proportions: An equation that states that two ratios are equal.
a c

b d
b and c are called the means AND a and d are called the extremes
Cross Products Property: In a proportion, the product of the extremes equals the product of
a c
the means.
If  where b  0 and d  0, then ad = bc
b d
Example 6: Solve proportions.
3 x

a.
4 16
3
2

x 1 x
b.
GEOMETRIC MEAN
The geometric mean of two positive numbers a and b is the positive number x that satisfies
a x.

x b
So, x2 = ab and x  ab
Example 7: Find the geometric mean of 16 and 48.
Checkpoint
2. Solve
8 2

y 5
3. Solve
4. Find the geometric mean of 14 and 16.
x  3 2x

3
9
```
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