Academic
Chapter 6 Notes
Ratios and
Proportions
Name____________Period_____
M3 Chapter 6 Notes: Sections 6.1-6.5
Vocabulary List:
Section 6.1:
 Ratio
 Equivalent ratios
Section 6.2:
 Proportion
Section 6.3:
 Cross product
Section 6.4:
 Similar figures
 Corresponding parts
 Congruent figures
Section 6.6:
 Scale drawing
 Scale model
 Scale
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M3 Chapter 6 Notes: Sections 6.1-6.5
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Section 6.1: Ratios and Rates
Learning Goals:
 We will write and simplify ratios.
 We will find the rates and unit rates.
Vocabulary:
 Ratio –
 Equivalent Ratios –
Example 1: Writing Ratios
Carmen tosses a foam ball at her waste basket. Out of 40 tosses, she
hits the basket 22 times and misses it 18 times. Write the ratio in
three ways.
a. The number of hits to the number of misses
b. The number of misses to the number of tosses
M3 Chapter 6 Notes: Sections 6.1-6.5
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Example 2: Comparing and Ordering Ratios
ON YOUR OWN:
A survey asked students whether they had after-school jobs. Write
each ratio as a fraction in simplest form.
Response
Number
Have a job
40
Don’t have a job
60
Total
100
a. Students with jobs to students without jobs
b. Students without jobs to all students surveyed
c. Which ratio is larger: students with jobs to all students
surveyed OR students without jobs to all students surveyed?
M3 Chapter 6 Notes: Sections 6.1-6.5
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Rates:
***A rate is a __________________________________________.
***A ____________________ has a denominator of ____________.
***Unit rates are often expressed in ________________________,
using the word ___________________.
Example 3: Finding a Unit Rate
ON YOUR OWN:
In one hour, 4 club members assemble 320 newsletters. What is their
assembly rate per person?
Example 4: Writing an Equivalent Rate
A jet flies 540 miles per hour. Write its rate in miles per minute.
ON YOUR OWN:
A car is traveling at 60 miles per hour. Write its rate in feet per
second.
M3 Chapter 6 Notes: Sections 6.1-6.5
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Example 5: Using Equivalent Rates
An insect crawls 1 foot in 10 seconds. At this rate, how far will it crawl
in 5 minutes?
ON YOUR OWN:
M3 Chapter 6 Notes: Sections 6.1-6.5
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Section 6.2: Writing and Solving Proportions
Learning Goal: We will write and solve proportions.
Example 1: Solving a Proportion Using Equivalent Ratios
Solve the proportion
5 x
 .
8 72
M3 Chapter 6 Notes: Sections 6.1-6.5
ON YOUR OWN:
Example 2: Solving a Proportion Using Algebra
Solve the proportion
x 3
 .
98 7
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M3 Chapter 6 Notes: Sections 6.1-6.5
ON YOUR OWN:
SETTING UP A PROPORTION:
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M3 Chapter 6 Notes: Sections 6.1-6.5
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Example 3: Writing and Solving a Proportion
During an outbreak of influenza, 2 students in Mrs. Show’s 2nd period
class were absent. There are 30 students taking this class. If the
same absentee rate is valid for the entire student population of 1200
students, write and solve a proportion to determine how many students
were absent from school during the outbreak.
ON YOUR OWN:
You know that 3 pizzas are enough to feed 12 people. Write and solve
a proportion to find the number of pizzas that will feed 28 people.
M3 Chapter 6 Notes: Sections 6.1-6.5
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Section 6.3: Solving Proportions Using Cross Products
Learning Goal: We will solve proportions using cross products.
Vocabulary:
 Cross product – the product of the numerator of one ratio and
the denominator of another ratio
***We can use cross products to tell whether two ratios form a
proportion. If the cross products are equal, then the ratios form a
proportion.
Example 1: Determining If Ratios Form a Proportion
ON YOUR OWN:
M3 Chapter 6 Notes: Sections 6.1-6.5
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*You can use the cross products property to solve proportions.
Example 2: Writing an Solving a Proportion
The worms in Janet’s compost bin can break down about 0.25 pound of
food scraps per day. How long would it take the worms to break down
8 pounds of food scraps?
ON YOUR OWN:
M3 Chapter 6 Notes: Sections 6.1-6.5
Extra Practice:
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M3 Chapter 6 Notes: Sections 6.1-6.5
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Basic Geometry Concepts
Learning Goal: We will prepare for solving problems that involve basic geometry concepts.
Points, Lines, and Planes
M3 Chapter 6 Notes: Sections 6.1-6.5
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Segments, Rays, and Angles
Example: Use the diagram to name two segments and their lengths,
two rays, and an angle and its measure.
Example: Use the diagram to name two segments and their lengths,
two rays, and an angle and its measure.
M3 Chapter 6 Notes: Sections 6.1-6.5
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Triangles, Quadrilaterals, and Congruent Parts
 Congruent segments –
 Congruent angles –
Example: Identify the angles, sides, congruent angles, and congruent
sides of the triangle.
M3 Chapter 6 Notes: Sections 6.1-6.5
Practice:
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M3 Chapter 6 Notes: Sections 6.1-6.5
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Section 6.4: Similar and Congruent Figures
Learning Goal: We will identify similar and congruent figures.
Vocabulary:
 Similar figures – figures that have the same shape but not
necessarily the same size
 Corresponding parts – a pair of sides or angles that have the same
relative position in two figures
M3 Chapter 6 Notes: Sections 6.1-6.5
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Example 1: Identifying Corresponding Parts of Similar Figures
ON YOUR OWN:
Example 2: Finding the Ratio of Corresponding Side Lengths
M3 Chapter 6 Notes: Sections 6.1-6.5
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ON YOUR OWN:
Given that FGHJ ~ KLMN , find the ratio of the lengths of the
corresponding sides of FGHJ to KLMN .
F
G
4
K
3
N
J
L
6
2
3
5
M
H
Example 3: Checking for Similarity
ON YOUR OWN:
The top of Selena’s rectangular dining room table measures 60 inches
by 108 inches. She has a matching rectangular coffee table whose top
measures 18 inches by 48 inches. Are the two tables similar?
M3 Chapter 6 Notes: Sections 6.1-6.5
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 Congruent figures – figures that have the same shape and the
same size. The corresponding parts are congruent.
Example 4: Finding Measures of Congruent Figures
ON YOUR OWN:
M3 Chapter 6 Notes: Sections 6.1-6.5
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Section 6.5: Similarity and Measurement
Learning Goal: We will find unknown side lengths of similar figures.
Example 1: Finding an Unknown Side Length in Similar Figures
ON YOUR OWN:
M3 Chapter 6 Notes: Sections 6.1-6.5
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Example 2: Using Indirect Measurement
(Hint: The cactus and man are perpendicular to the ground. The sun’s
rays strike the cactus and the man at the same angle, forming two
similar triangles.)
ON YOUR OWN:
Example 3: Using Algebra and Similar Triangles
M3 Chapter 6 Notes: Sections 6.1-6.5
ON YOUR OWN:
Find the length of DE .
Extra Practice:
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