Chapter 5

Proportions and Similarity

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5.1B Rates

I can determine unit rates.

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Vocabulary:

Rate – ratio that compares two quantities with different units

Unit rate – rate that is simplified so that the denominator is 1 unit

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Example: Michaela earned $12 in 2 hours, how much would she earn in 1 hour?

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Example; If 3 pounds of tomatoes cost $6, how much would 1 pound cost?

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If 8 pounds of dog food cost $12, how much will 1 pound cost?

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Example: Ty painted 3 faces in 12 minutes at the Fall Fest. At this rate, how many faces can he paint in 40 minutes?

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Homework:

p. 269 #7-23

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5.1C Proportional and Nonproportional Relationships I can identify proportional and nonproportional

relationships.

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Vocabulary:

Proportional – two quantities that have a constant ratio

Nonproportional – two quantities that do not have a constant ratio

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Example: What is the ratio of each y-value to itscorresponding x-value? Is y proportional to x? Explain

x 2 4 6 8 10

y 3 6 9 12 15

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Example: A cleaning service charges $45 for the first hour and $30 for each additional hour. Is the fee proportional to the number of hours worked? Make a table of values to explain your reasoning.

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Example: A recipe for jelly frosting calls for 1/3 cup of jelly and 1 egg white. Is the number of egg whites used proportional to the cups of jelly used? Make a table of values to explain your reasoning.

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Example: An adult elephant drinks about 225 liters of water each day. Is the number of days that an elephant’s water supply lasts proportional to the number of liters of water the elephant drinks? Explain your answer with a table.

LSowatsky 15This Photo by Unknown Author is licensed under CC BY-SA

Homework:

p. 274 #5 - 13

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5.1D Solve Proportions

I can use proportions to solve problems.

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7.RP.1, 7.RP.2, 7.RP.2b, 7.RP.2c, 7.RP.3

Vocabulary:

Equivalent ratios: ratios that have the same value

Proportion: equation stating that two ratios or ratesare equivalent.

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Cross Products:

The cross products of any proportion are equal.

Can use cross products to solve proportions

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Example: Solve the proportions.

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9

4 10

x

2 5

24 y

Example: Brenic can decorate 8 t-shirts in 3 hours. Write and solve a proportion to find the time it will take him to decorate 20 t-shirts at this rate.

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Example: A recipe serves 10 people and calls for 3 cups of flour. If you want to make the recipe for 15 people, how many cups of flour should you use?

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Example: Haley bought 4 pounds of tomatoes for $11.96. Write an equation relating the cost to the number of pounds of tomatoes. How much would Haley pay for 6 pounds at this same rate? For 10 pounds?

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Homework:

p.279 #6 – 21, 23

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5.2B Scale Drawings

I can solve problems involving scale drawings.

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Vocabulary: Scale drawings: 2-dimensional representation or

drawing used to represent an object that is too large or too small to be drawn at actual size.

Scale model: a representation of an object that is toolarge or too small to be built at actual size.

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Examples of scale drawings/models:

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This Photo by Unknown Author is licensed under CC BY-SA

This Photo by Unknown Author is licensed under CC BY-NC-SA

This Photo by Unknown Author is licensed under CC BY-SA

Scale factor:

A scale written as a ratio without units in simplest form.

Example: find the scale factor of 1/4inch to 2 feet

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Example: An artist is painting a large mural of flowers on the side of a school. If she uses the scale 4 inches = 1 inch, how large will the mural painting of a rose bloom be if it is 6 ¼ inches high.

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Example: Find the scale factor of a blueprint if the scale is ½ inch = 3 feet.

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Example: An architect is making a model of an apartment building that is 150 feet tall. Find the scale if the model of the apartment building is 3 inches tall. Then, find the height of the model of a house nearby if the actual height is 25 feet.

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Homework:

p. 287 #1 - 18

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5.3A Similar Figures

I can solve problems involving similar figures.

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Vocabulary:

Similar figures – figures that have the same shape but not necessarily the same size

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Corresponding sides:

Corresponding angles:

Similar Figures

Two geometric figures are similar if the following condition are true:

• Both figures are the same shape.

● The corresponding angles of the figures are congruent.

● The ratios of the lengths of corresponding sides are equal, so they form a proportion.

Two figures that have the same shape but not necessarily the same size are similar.

Two polygons are similar if:1. corresponding angles are congruent.2. corresponding sides are proportional.

notation:’ ~’ means similar

Definition of Similar Figures In mathematics, figures are said to be similar if their

corresponding angles are congruent (equal) and their corresponding sides are in proportion.

We can use the definition of similarfigures to find missing measurements:

How?

Use proportions

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Example: Using Similar Polygons

Quadrilateral JKLM is similar to PQRS. Find the value of z.

Set up a proportion that contains PQ

15

10J

M L

K

Z

6

S

PQ

R

Example: The triangles are similar. Find the missing values using proportions.

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Example: At a certain time of day, a cabbage palm tree that is 71 feet high casts a shadow that is 42.6 feet long. At the same time, a nearby flagpole casts a shadow that is 15 feet long. How tall is the flagpole?

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Homework:

p. 296 #1 - 12

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Chapter Test

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