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6-8 Accelerated 7 Unit 8 Lesson 7

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K-5 Math •6-8 Math 9-12 Math

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Accelerated 6 •Accelerated 7

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Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 •Unit 8 Unit 9

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 •Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15

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IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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Unit 8, Lesson 7

A Proof of the Pythagorean Theorem

Accelerated 7

Practice

Problem 1

Use the areas of the two identical squares to explain why \(5^2+12^2=13^2\) without doing any calculations.

2 decomposed squares.

to access Practice Problem Solutions.

Lesson 7 Resources

Student Materials

Problem 2

Find the exact value of each variable that represents a side length in a right triangle.

5 right triangles.

to access Practice Problem Solutions.

Problem 3

In each part, \(a\) and \(b\) represent the length of a leg of a right triangle, and \(c\) represents the length of its hypotenuse. Find the unknown length, given the other two lengths.

\(a=3, b=1, c={?}\)
\(a={?}, b=2, c=\sqrt{29}\)
\(a=\sqrt5, b=\sqrt7, c={?}\)
\(a=\sqrt8, b={?}, c=\sqrt{13}\)
\(a={?}, b=\sqrt{13}, c=4\)

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Problem 4

ForLesson 13: Adding and Subtracting with Scientific Notation

In 2015, there were roughly \(1 \times 10^6\) high school football players and \(2 \times 10^3\) professional football players in the United States. About how many times more high school football players are there? Explain how you know.

to access Practice Problem Solutions.

Problem 5

ForLesson 5: Square Roots on the Number Line

Each number is between which two consecutive integers?

\(\sqrt{10}\)
\(\sqrt{54}\)
\(\sqrt{18}\)
\(\sqrt{99}\)
\(\sqrt{41}\)

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