Name: Date: Period: Topic: Proportions and Similar Figures Essential Question: What strategy would best assist me on finding missing lengths or values of figures/problems?

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NameDatePeriod Topic Proportions and
Similar FiguresEssential Question What
strategy would best assist me on finding missing
lengths or values of figures/problems?
VocabularyProportions
if two ratios are equal, they form a proportion.

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Proportion Examples





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describes things which have the same shape but
are not the same size.
Similar Figures
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Similar Shapes

• Similar shapes are very important. This is
  because if we know the dimensions of one shape
  and one of the dimensions of another shape
  similar to it, we can figure out the unknown
  dimensions.

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Visual Example

• These two stick figures are similar. As you can
  see both are the same shape. However, the bigger
  stick figures dimensions are exactly twice the
  smaller.
• So the ratio of the smaller figure to the larger
  figure is 12 (said one to two). This can also
  be written as a fraction of ½.

8 feet
4 feet
2 feet
4 feet
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Solving Proportional Problems

• So how do we use proportions and similar figures?
• Using the previous example we can show how to
  solve for an unknown dimension.

8 feet
4 feet
2 feet
? feet
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Solving Proportion Problems

• First, designate the unknown side as x. Then,
  set up an equation using proportions. What does
  the numerator represent? What does the
  denominator represent?
• Then solve for x by cross multiplying

8 feet
4 feet
2 feet
4x 16 X 4
? feet
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Try One Yourself

• Knowing these two stick figures are similar to
  each other, what is the ratio between the smaller
  figure to the larger figure?
• Set up a proportion. What is the width of the
  larger stick figure?

12 feet
HINT Set the proportion based on equivalent sides
x feet
8 feet
4 feet
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Try Another
? feet
4 feet
8 feet
3 feet
Our friends the aliens are back ?
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Proportions and Triangles

• What are the unknown values on these triangles?

20 m
16 m
x m
y m
First, write proportions relating the two
triangles.
4 m
Then, solve for the unknown by cross multiplying.
3 m
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Triangles in the Real World

• Do you know how tall your school building is?
• There is an easy way to find out using right
  triangles.

To do this create two similar triangles using the
building, its shadow, a smaller object with a
known height (like a yardstick), and its
shadow. The two shadows can be measured, and you
know the height of the yard stick. So you can set
up similar triangles and solve for the height of
the building.
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Solving for the Buildings Height

• Here is a sample calculation for the height of a
  building

building
x feet
48 feet
yardstick
3 feet
4 feet
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Challenge?!?

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Pair-Practice

• Page 127 (12, 14,16, 28, 32, 34)
• Page 129 (60)
• Page 134 (8, 10, 14, 15, 17)
• Page 135 (23)

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Independent Practice

• Page 134 (9)
• Page 136 (31, 35, 36, 37, 38,39)

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Wrap-Up

• Reminder
• Vocabulary Review, Write your summary Create
  Left Side Notes
• Home-Learning Assignment 8
• Page 121 (2, 12, 14, 18)
• Page 127 (3, 4, 10, 11)
• Page 136 (32, 33)