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# Pythagorean Theorem proof

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## Joe Rosenbrock

on 14 April 2014

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#### 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?
=
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.
Full transcript