Pythagorean Theorem

Pythagorean Theorem

John Welkener, M. Ed.

February 2022​

Success Criteria

I can:

• Identify the components of a right triangle.

• Use the Pythagorean Theorem to measure distances in real-world scenarios.

The above criteria align with Alaska Mathematics Standards 8.G.6, 8.G.7, 8.G.8, and 9-12.G-SRT.4

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• Greek philosopher and mathematician

• Influenced many great scientists, including Aristotle, Newton, and Einstein

• Gets credit for the Pythagorean Theorem (although the Babylonians knew about it 1000 years earlier)

Pythagoras

(570 - 495 B.C.)​

Squares practice

​In your graphic organizer:

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1. Use a yellow marker to count ​the squares on the left side.

2. Use a blue marker to count the squares on the bottom.​

3. Use a green marker to count ​the squares on the long side.​

Squares practice

​In your graphic organizer:

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1. ​How many yellow squares​ are there?

2. How many blue squares?

3. How many green squares?

4. What is the sum of yellow squares + blue squares?

5. Now, compare the sum of yellow + blue squares to the sum of yellow squares.

   What do you notice?

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Pythagorean Theorem

a² + b² = c²

Right triangles have one angle that is 90 degrees.

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​The theorem only works on right triangles.​

Pythagorean Theorem

a² + b² = c²

The Pythagorean Theorem is used to identify the missing side of a right triangle.

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In the right triangle above, notice that the sum of yellow and blue triangles equals the sum of the green triangles.

This is one of many popular proofs of the Pythagorean Theorem.

Multiple Select

Select which triangle(s) are right triangles.

• Triangle 1

• Triangle 2

• Triangle 3

Multiple Choice

The Pythagorean Theorem is used to

• measure the angle of a triangle.

• identify the missing side of a right triangle.

Multiple Choice

In the formula $$a^2+b^2=c^2$$  , the letters $$a$$   and $$b$$   represent:

• the legs of a right triangle

• the hypotenuse of a right triangle

Multiple Choice

In the formula $$a^2+b^2=c^2$$  , the letter $$c$$  represents:

• the legs of a right triangle

• the hypotenuse of a right triangle

Multiple Choice

$$a^2\ =$$   

• $$a\times a$$  

• $$a+a$$  

• $$b^2$$  

• c

Multiple Choice

Write $$5\times5$$  as an exponent

• 5²

• 10

• 25²

• 25

Multiple Choice

Write 3 $$\times$$   3 as an exponent.

• 3²

• 9²

• 9

• 6

Multiple Choice

Write c $$\times$$   c as an exponent.

• c²

• d²

• 9

• a

Pythagorean Triples

Copy the chart on the right into your graphic organizer.

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Use these to determine the missing side on the next few questions.​​

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PRO TIP: These are the three best-known 'Pythagorean triples'. You can derive more Pythagorean triples by multiplying the set by any integer. For example, if you multiply the set (5, 12, 13) by 2, you get (10, 24, 26), which also satisfies the Theorem.

Multiple Choice

What is the length of the hypotenuse?

c = _ meters

• 6

• 5

• 2

• 10

Multiple Choice

What is the length of the hypotenuse?

c = _ meters

• 5

• 6

• 8

• 10 meters

Multiple Choice

Stu takes a sheet of paper and cuts from one corner to the opposite corner, making two triangles. If the piece of paper is 5 inches long and 12 inches wide, how long is the diagonal cut that Stu made?

• 12 inches

• 8 inches

• 13 inches

• 14 inches

Real-world application

Let's apply Pythagorean to these 2 scenarios:

1. Measuring the diagonal of a tarp.

2. Measuring distance traveled along a trapline.

Group activity: tarp measurement

1. Measure and record the width of the tarp in inches.

2. Measure and record the height of the tarp in inches.

3. Now, use Pythagorean Theorem to calculate the diagonal length of the tarp in inches. Round your answer to the nearest tenth.

Open Ended

How many inches long is the diagonal of the tarp? __ inches.

Multiple Choice

Steven walks 30 paces due east from his cabin to his trapline. He then walks 40 paces due south along his trapline. If he takes the shortcut back to his cabin, how many paces does Steven need to walk?

• 70 paces

• 50 paces

• 60 paces

• 40 paces

More applications

How could we apply Pythagorean in the following situations?

• Setting snares

• Playing basketball

• Walking to the Post Office

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Open Ended

Can you think of any more real-world scenarios where Pythagorean Theorem could be applied? List any you can think of in the box below.

Open Ended

In your own words, type 1-3 sentences about what you learned from this lesson.