Pythagorean Theorem Review

Pythagorean Theorem Review

Multiple Choice

Pythagorean Theorem only works on one type of triangle. What kind of triangle does it have to be?

• Acute

• Right

• Obtuse

Hypotenuse- the longest side of a right triangle. This side is always "c"

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Legs- the two sides that create the right angle. "a" and "b"​

Sides of a Triangle

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Multiple Choice

Which side is the hypotenuse?

• this side

• that side

• this other side

This equation can help us find the missing side of a right triangle.

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We can also use it to determine if a triangle is a right triangle or not since it only works for right triangles. ​

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Multiple Choice

Which equation below is a correct interpretation of the Pythagorean Theorem for the right triangle pictured on the left? Remember, the hypotenuse is always the longest side of a right triangle.

• $$x^2+y^2=z^2$$  

• $$y^2+x^2=z^2$$  

• $$x^2+z^2=y^2$$  

• $$y^2+z^2=x^2$$  

Multiple Choice

In the right triangle pictured on the left, which of the following equations will allow you to successfully solve for the unknown x?

• $$8^2+x^2=4^2$$  

• $$4^2+8^2=x^2$$  

• $$x^2+8^2=4^2$$  

• $$x^2+4^2=8^2$$  

Multiple Choice

In the right triangle pictured on the left, which of the following equations will allow you to successfully solve for the unknown x?

• $$12^2+16^2=x^2$$  

• $$12^2+x^2=16^2$$  

• $$16^2+x^2=12^2$$  

• $$x^2+12^2=16^2$$  

​ 1. Write your equation

2. Square your numbers

3. Combine like terms

4. Take the Square Root​

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Solving for the hypotenuse

1. Write the equation

2. Square your numbers

3. Subtract to get variable alone

4. Take the square root​

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Solving for a leg

Multiple Choice

Which equation would you use to solve for x?

• $$6^2+x^2=8^2$$  

• $$6^2+8^2=x^2$$  

• $$x^2+8^2=6^2$$  

Fill in the Blanks

Use the pythagorean theorem to find the missing side length.

Multiple Choice

Which equation would you use to solve for x?

• $$13^2+x^2=5^2$$  

• $$5^2+13^2=x^2$$  

• $$x^2+5^2=13^2$$  

Because we have to end each problem by taking the square root of a number, the answers are not always whole numbers. If the question asks for an exact answer, leave it as a radical. If it asks for a rounded, be sure to round to whatever place it asks for.

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Exact vs Rounded

​​Rounded Answer

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​​Exact Answer

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Multiple Choice

Determine the length of the missing side.

• 7

• 8

• 17

• 23

Multiple Choice

Find the length of the missing side. 

• 48 in.
• 52 in.
• 16 in.
• 24 in.

Multiple Choice

Find side "h" (wall height)

• 35.60

• 35.00

• 35.71

• 61.03

Multiple Choice

^{Find the length of the missing side}

• 48

• 108

• 83.6

• 72