Properties of Proportions

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Properties of Proportions

• 7-2

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EXAMPLE 4
Use a scale drawing
SOLUTION
Use a ruler. The distance from Pocahontas to
Algona on the map is about 1.25 inches. Let x be
the actual distance in miles.
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EXAMPLE 4
Use a scale drawing
Cross Products Property
Simplify.
The actual distance from Pocahontas to Algona is
about 32.5 miles.
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EXAMPLE 5
Solve a multi-step problem
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EXAMPLE 5
Solve a multi-step problem
SOLUTION
Cross Products Property
Solve for x.
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EXAMPLE 5
Solve a multi-step problem
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for Examples 4 and 5
GUIDED PRACTICE
4. Two cities are 96 miles from each other.
The cities are 4 inches apart on a map. Find the
scale of the map.
SOLUTION
The distance between two cities are 96 miles, and
the distance on the map is 4 inches
Simplify.
1 24
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for Examples 4 and 5
GUIDED PRACTICE
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for Examples 4 and 5
GUIDED PRACTICE
5. What If ? Your friend has a model of the
Reunion Tower that is 14 inches tall. What is the
diameter of the dome on your friends model?
SOLUTION
Cross Products Property
Solve for x.
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EXAMPLE 1
Use properties of proportions
SOLUTION
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EXAMPLE 1
Use properties of proportions
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EXAMPLE 2
Use proportions with geometric figures
SOLUTION
Given
Property of Proportions (Property 4)
Substitution Property of Equality
Cross Products Property
Solve for x.
So, BA 12 and BD 12 3 9.
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EXAMPLE 3
Find the scale of a drawing
SOLUTION
To find the scale, write the ratio of a length in
the drawing to an actual length, then rewrite the
ratio so that the denominator is 1.
The scale of the blueprint is 2.5 cm 1 cm.
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for Examples 1, 2 and 3
GUIDED PRACTICE
1. In Example 1, find the value of x.
SOLUTION
Write proportion
Substitute.
Cross Product property
Multiply
Divide
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for Examples 1, 2 and 3
GUIDED PRACTICE
2. In Example 2, find the
value of x.
SOLUTION
Given
Property of Proportions (Property 4)
Substitution Property of Equality
Cross Products Property
Solve for AC.
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for Examples 1, 2 and 3
GUIDED PRACTICE
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for Examples 1, 2 and 3
GUIDED PRACTICE
3. What If ? In Example 3, suppose the length
of the antenna on the blueprint is 10
centimeters. Find the new scale of the blueprint.
SOLUTION
To find the scale, write the ratio of a length in
the drawing to an actual length, then rewrite the
ratio so that the denominator is 1.
The scale of the blueprint is 5 cm 1 cm.