Chapter 7 Similarity

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Chapter 7Similarity

• Sec. 7 1
• Ratios Proportions

Objectives 1) To write ratios and
solve proportions.
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Ratio A comparison of 2 quantities.

• Can be written as
• a to b
• ab
• a/b

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Ex1 Writing a ratio

• The length of a model car is 4in long. The
  actual length of the car is 15ft long. What is
  the ratio of the length of the model to the
  length of the actual car?

Reduce
4in
1in
4in
4in


1 to 45

45in
15(12in)
180in
15ft
Must have same units in numerator as in the
denominator!! Convert feet to inches by
multiplying by 12in.
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Proportion A statement that sets two ratios
equal to each other.

• Can be reduced to the same fraction.
• Write it as

a
c
a
c


b
d
b
d
Cross-Products ad bc
Ratio 1
Ratio 2
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In Algebra 1 you learned the Cross Products
Property. The product of the extremes ad and the
product of the means bc are called the cross
products.
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extra - fyi
The following table shows equivalent forms of the
Cross Products Property.
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Example Solving Proportions
Solve the proportion.
Cross Products Property
7(72) x(56)
Simplify.
504 56x
Divide both sides by 56.
x 9
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Ex.2 Solve each Proportion

2
n
(x1)
x


5
35
3
2
Find the cross products (Cross multiply Divide)
Step 1 Find the cross products! 2(x1) 3x 2x
2 3x 2 x
2(35) 5n 70 5n n 14
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Scale Drawings

• The scale is usually located at the bottom of the
  map or in the legend.
• The scale is a ratio
• You will use it to set up a proportion to solve a
  problem.
• Problem like How many miles is Denver from
  Louisville?
• It usually looks like
• 1in 50miles
• 2cm 80km

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Example 3 Use proportions to solve the
following problem.

• 2 cities are 3.5in apart on a map. The scale is
  1in 50miles. Find the actual distance.
• Step 1 Set up the proportion with the scale as
  one ratio and the actual distances as the other.
  Keep like units in proper places.

Inches on top
1in
3.5in
Miles on bottom

50mi
x mi
Find the cross Products or cross-multiply and
divide.
Scale ratio
Actual Ratio
1x 50(3.5) x 175 miles
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Example Problem-Solving Application
The answer will be the length of the room on the
scale drawing.
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Example Continued
Let x be the length of the room on the scale
drawing. Write a proportion that compares the
ratios of the width to the length.
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Example Continued
Cross Products Property
5(15) x(12.5)
Simplify.
75 12.5x
Divide both sides by 12.5.
x 6
The length of the room on the scale drawing is 6
inches.