Name ________________________________________
Period_______
In the past few lessons, you enlarged and reduced images while preserving
their shapes. By doing so, you created similar figures. You learned, for
example, that to enlarge a shape to 300% of the original, you multiplied the
length of each side by 3.
If you want to compare side lengths of similar figures, one way to do so is by
using ratios. A ratio compares lengths by dividing. In this lesson, you will
learn about using ratios to determine whether enlargements or reductions
were done correctly. As you work with your team, use the questions below
to help start your discussions.
How does the shape change?
What are we comparing?
How can we describe the relationship?
4-63. Andrew, Barb, Carlos, and Dolores
were looking at the similar triangles at
right. “Similar” in this context means that
the triangles have the same shape, but they
are different sizes.
“I’m confused,” said Carlos. “Is the
triangle on the right an enlargement of
the triangle on the left, or is the triangle on
the left a reduction of the triangle on the right?”
a. Work with your team to find a way to describe the relationship between the
lengths of the sides of these two triangles. Think about how each triangle
might have been created from the other one. Be prepared to share your
ideas with the class.
b.“Hey,”Barb said, “I just learned about ratios from my sister. She told me
that ratios are another way to compare quantities like the dimensions of
these triangles. We could compare these triangles by setting up the ratio of
𝟒
4 units to 10 units. We can write it in these ways.” 4:10 𝟏𝟎 4 to 10
Carlos wondered, “But wait, why wouldn’t the ratio be 6 to 15?”
i. Where did Barb and Carlos get the numbers that they are using in their
ratios? What are they comparing?
ii. Whose ratio is correct? How do you know?
iii. What are some other ratios that represent the same relationship as
4:10? Work with your team to find at least three other ratios and be
prepared to share them with the class.
c. Dolores was confused and wondered, “Why isn’t the ratio 10:4?”
What would you say in response to her question?
d. Is the ratio 2:5 the same as Barb’s ratio of 4:10? Why or why not?

4-65. You may remember that a quadrilateral is a four-sided figure. There 
are many different kinds of quadrilaterals. On graph paper, draw a
quadrilateral with one side that is 12 units long and another side that is
9 units long. Then reduce your quadrilateral so that the ratio of sides of
new to original is 2 to 3.


Carlos says that the base of triangle B must be 25 units long, because 25 is
halfway between 5 and 45. Is he correct? If so, explain how you can be
sure. If not, what is the length of the base of triangle B? How do you
know?
4-68. You have discovered that when you enlarge a figure, the ratio of side
lengths between the original and the enlargement stay the same. What
about the perimeters? What about the areas? When you enlarge a
figure, does the ratio of the perimeters between the original and the
enlargement stay the same, too? What about the ratio of
the areas? Think about this as you conduct the following investigation.
a. Find the perimeter and area of the rectangle at right.
4-66. Xenia drew the trapezoid shown below. She wants to draw another
figure of the same shape so that the relationship between the two figures
2
can be described by a ratio of 2 to 7 or 7 .
What will be the length of the longest side of her
new shape? Is there more than one possibility for
her new shape?
4-67. TEAM CHALLENGE- Carlos was working with his team to solve the
following challenge problem.
Triangles A, B, and C are shown here. The ratio of the
sides of triangle A to triangle B is the same as the ratio of
the sides of triangle B to triangle C.
b.What is the length and width of a new rectangle that is an enlargement of
the rectangle at above, so that the ratio of the sides of the original rectangle
to the new one is 2:3 ?
Length-
Width-
c. Find the perimeter and area of the new, larger rectangle.
Perimeter-
Area-
d.
Write the ratio of the original perimeter to the new perimeter. Then
write the ratio of the original area to the new area. Are the ratios the same?
4-73. A new shipment of nails is due any day at Hannah’s Hardware Haven,
and you have been asked to help label the shelves so that the nails are
organized in length from least to greatest. She is expecting nails of the
4-69. LEARNING LOG-Today you learned about a different way to
compare similar figures, by using a ratio. Write a Learning Log entry
in your TOOL KIT describing what you know so far about
ratios. Include the different ways that ratios can be written. Also
include an example of how you can use a ratio to enlarge or reduce a
figure. Label the entry “Ratios”.
Lesson 4.2.3 HOMEWORK
COMPLETE THIS IN YOUR HOMEWORK NOTEBOOK!
DO NOT COMPLETE HOMEWORK ON THIS SHEET!
3
7
1
7
1
following sizes:1 inch, 1 inch, 2 inch, inch, and 1 inch. Use the
8
8
4
8
2
ruler below to help Hannah order the labels on the shelves from least to
greatest.
4-74. Cecelia wants to measure the area of her bedroom floor. Should she
use square inches or square feet?
a. Write a sentence to explain which units you think Cecelia should use.
4-70. On graph paper, draw any quadrilateral. Then enlarge (or reduce) it by
each of the following ratios.
b. If Cecelia’s bedroom is 12 feet by 15.5 feet, what is the area of the
bedroom floor? Show how you got your answer.
a.
c. Find the perimeter of Cecelia’s bedroom floor. Show how you got your
answer.
b.
4-71. George drew the diagram at right to represent the number
“Look,” said Helena, “This is the same thing as
12
5
.”
What do you think? Explore this idea in parts (a) through (c) below.
a. Is Helena correct? If so, explain how she can tell that the diagram
represents
12
5
. If she is not correct, explain why not.
2
b. Draw a diagram to represent the mixed number 3 .
3
How can you write this as a single fraction greater than one?
7
c. How can you write as a mixed number? Be sure to include a diagram in
4
your answer.
4-72. Simplify the following expressions.
a.
b.
c.