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How do you know whether two dimensional shapes are similar?
For example:
Jen’s bedroom is 30 feet long and 20 feet wide. Her soccer field is 120 yards long and 80 yards
wide. Is Jen’s bedroom similar to her soccer field?
In this lesson you will learn how to determine whether two dimensional shapes are similar by testing whether the shapes
have the same number of sides, the same ratio between
dimensions, and the same ratio within dimensions.
Let’s Review
Between Ratio Within Ratio
20 2 6 60
20 2 6 60
Let’s Review
Similar Shapes
Number of Sides
Same
Similar
BetweenRatios
Same
Similar
WithinRatios
Same
Similar
A Common Mistake
What characteristics make shapes similar?
Color Shape Size
Core Lesson
Jen’s bedroom is 30 feet long and 20 feet wide. Her soccer field is 120 yards long and 80 yards wide. Is Jen’s bedroom similar to
her soccer field?
30 feet
20 feet
120yards
80 yards
Core Lesson
Is the number of sides the same?
4 4 sides sides
Yes
Core Lesson
Is the ratio between the shapes the same?
Yes
Width of bedroom : Width of soccer field
Length of bedroom : Length of soccer field
Core Lesson
Width of bedroom : Length of bedroom
Is the ratio within the shapes the same?
Yes
Width of soccer filed : Length of soccer field
Core Lesson
Similar Shapes
Number of Sides
Same
Similar
BetweenRatio
Same
Similar
WithinRatio
Same
Similar
In this lesson you have learned how to determine whether two dimensional shapes are similar by testing whether the shapes
have the same number of sides, the same ratio between
dimensions, and the same ratio within dimensions.
Guided Practice
Jamie’s living room is 45 feet long and 15 feet wide. Her field hockey field is 180
yards long and 60 yards wide. Is Jen’s living room similar to her field hockey field?
15 feet
45 feet
180 yds
60 yds
Extension Activities
Measure the dimensions of at least ten different rectangular surfaces. Are any of the rectangular surfaces similar? Use diagrams, ratios, and written descriptions to justify your answer and explain your thinking.
Extension Activities
Research the golden ratio and create a presentation of your findings to share with your classmates. Be sure to include what the golden ratio is, what a rectangle with the golden ratio would look like, how to draw a rectangle with the golden ratio, at least 3 examples of where the golden ratio can be found, and how the golden ratio relates to the Fibonacci series.
Quick Quiz
Joe’s classroom is 30 feet long and 6 feet wide. His football field is 150 feet long and 30 feet wide. Is Joe’s bedroom similar to his football field?
John’s bathroom is 20 feet long and 5 feet wide. His basketball court is 160 feet long and 40 feet wide. Is John’s bedroom similar to his basketball court?
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