Pythagorean Theorem Proof Without Words


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.  

This puzzle is a great little project or activity to help students understand the Pythagorean Theorem!  The proof could easily be added to an interactive notebook for foldable for students as well.  I love proofs like this for geometry!

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

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

Perigal's Puzzle: A Pythagorean Theorem Proof Without Words

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

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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