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Name_____________________________________ Class____________________________ Date________________
Lesson 8-1 (pp. 416–419)
Ratios and Proportions
Lesson Objective
1 Write ratios and solve proportions
NAEP 2005 Strand: Geometry
Topic: Position and Direction
Local Standards: ____________________________________
Vocabulary and Key Concepts.
Properties of Proportions
(1) ad bc
(2) ba d
c
(3) ac b
d
b
(4) a 1
b c1d
d
A proportion is a statement that two ratios are equal.
a
c
b d and a : b c : d are examples of proportions.
All rights reserved.
a
c
b d is equivalent to
An extended proportion is a statement that three or more ratios are equal.
6
4
1
24 16 4 is an example of an extended proportion.
The Cross-Product Property states that the product of the extremes of a proportion is equal
means
a:b c:d
a
c
b d
a d b c
extremes
A scale drawing is a drawing in which all lengths are proportional to corresponding actual
lengths.
A scale is the ratio of any length in a scale drawing to the corresponding actual length.
The lengths may be in different units.
Examples.
1 Finding Ratios A scale model of a car is 4 in. long. The actual car is 15 ft
long. What is the ratio of the length of the model to the length of the car?
Write both measurements in the same units.
180
15 ft 15 12 in. in.
length of model
4 in.
4 in.
4
length of car 5 15 ft 5 180 in. 5 180 5
1
45
The ratio of the length of the scale model to the length of the car is
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Lesson 8-1
1
:
45 .
Geometry Daily Notetaking Guide
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to the product of the means.
GeomPHM5e_DNG_142-158
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Name_____________________________________ Class____________________________ Date ________________
2 Properties of Proportions
b
Complete: If a4 5 12
b , then 12 5
48
ab 5
ab
.
Cross-Product Property
48
12a
12a
12a
Divide each side by
.
4
b
12 5
Simplify.
a
3 Solving for a Variable Solve each proportion.
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a.
25 n
5
35
5n 5 2
(
35
)
Cross-Product
5n 5
70
Simplify.
n5
14
Divide each side by 5 .
1
x
b. x 1
3 52
3x 5 2
3x 5
(
2x
x 1 1
1 2
x5 2
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
)
Subtract
Property
Cross-Product
Property
Distributive
Property
2x
from each side.
Check Understanding.
1. A photo that is 8 in. wide and 513 in. high is enlarged to a poster that is 2 ft
wide and 113 ft high. What is the ratio of the height of the photo to the height
of the poster?
1:3
n
2. Write two expressions that are equivalent to m
4 5 11.
4 5 11, m 1 4 5 n 1 11
Answers may vary. Sample: m
n
4
11
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Page 144
Name_____________________________________ Class____________________________ Date ________________
Example.
4 Using Proportions Two cities are 3 12 in. apart on a map with the scale
1 in. 50 mi. Find the actual distance.
Let d represent the actual distance.
map distance (in.)
actual distance (mi.) 5
1
Substitute.
50
d 5 50
d5
(
31
2
175
The cities are actually
)
Cross-Product
Property
Simplify.
175
All rights reserved.
d
miles apart.
Check Understanding.
3. Solve each proportion.
a. 5z 5 20
3
z 0.75
6
b. n 18
165n
n3
4. Recall Example 4. You want to make a new map with a scale of 1 in. 35 mi.
Two cities that are actually 175 miles apart are to be represented on your map.
What would be the distance in inches between the cities on the new map?
5 inches
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Lesson 8-1
Geometry Daily Notetaking Guide
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31
2
1 in.
50 mi