#### Transcript of Pythagorean Theorem proof

**Pythagorean Theorem Proof**

Triangles Have Many Properties

Lets Get Started

Cut out the shapes from the worksheet

Finding Area

Determine the Area of each shape you just cut out

Arrange these shapes so they fit inside the big green square.

Create as many different ways the shapes can be arranged within the large green square.

[hint: you will not use every shape in every arrangement]

I Picked these two

But Before We can Use it...We must prove it!

The Pythagorean Theorem Applies to Right Triangles

Remember:

GO AHEAD! Determine the area of each shape.

Write the Area on the shape

So.......what did you get?

Area =

(1/2)ab

Here are a few Arrangements

Now

Pick two of the arrangements you created that are the most different from each other.

the proof will still work if you don't chose these two exactly

you will need this arrangement for sure

Can you see what different shapes are equal to each other?

Look at your arrangements

=

Notice both are equal in area

=

By taking away from each

=

What did I do here?

All the were taken away

we can do this because each has

the same area. So taking away the same

amount (4 ) from each side is okay to do.

Now Compare the Areas of the remaining shapes

=

Where a, b, and c are the lengths of a right triangle

And that's the Proof!

YOU DID IT!!!

This is what we just did...See if you can follow along.

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