Pythagorean Theorem Proof Without Words

10 January 2016

By the time my students reach me, they have already heard of the Pythagorean Theorem.  However, when I introduce right triangles, I always start with a lesson on the Pythagorean Theorem.  I find that many students don’t understand where it comes from and just take it blindly as a formula.  

I like to show my students Perigal’s Puzzle.  Basically, it is a proof without words of the Pythagorean Theorem.  First, you start with a right triangle.

A Pythagorean Theorem Proof Without Words | mrseteachesmath.blogspot.com

Then, you have the areas of each side: a^2, b^2, and c^2.  To make things easy, I will call them Square A, Square B, and Square C.

Perigal's Puzzle: A Pythagorean Theorem Proof Without Words | mrseteachesmath.blogspot.com

Perigal's Puzzle: A Pythagorean Theorem Proof Without Words | mrseteachesmath.blogspot.com

Cutting apart Square B, you can fit Squares A and B to be the same as Square C.

Perigal's Puzzle: A Pythagorean Theorem Proof Without Words | mrseteachesmath.blogspot.com

BAM!  The Pythagorean Theorem works.  

Here is a file that you can download for easy cutting :)  Also, if cutting paper isn’t your style, there is a YouTube video you can show.


Enjoy!

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2 comments:

  1. This is really great. I think I will print Square A, Square B and Square C in separate colors. It makes more sense to me to be able to see the different parts of Square A and Square B when they are placed together.

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