# Pythagorean Theorem - Paper Proof and Design Challenge

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7 MB|6 pages
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This math assignment is half geometry and half art. An appropriate lesson for geometry, algebra or pre-algebra. It is a proof of the Pythagorean Theorem without numbers.

Students start with a large paper square and divide up the space on the front and back with the necessary squares, triangles, and lines. Adding labels and folds will aid in demonstrating the proof. You may find different versions of this lesson on the net. But it is unlikely you will find anything which puts the math and visual examples together the way I do. It is much easier to understand the proof this way.

The ideal supplies needed to teach this are blank white paper, rulers, scissors, and colored pencils. If you let them use rulers, it makes this more of an applied geometry design challenge. Using their creativity to make the paper proof based on what they learned in your class and the drawings included in this lesson file. You should create one yourself and bring it in as a visual example of what they are supposed to create. Let them pass it around, and then challenge them to accurately recreate the same thing based on any geometry method that works. It is really not that easy to recreate this accurately and line up the shapes on the front and back side. Let the kids surprise you with their creativity, and also get some exposure to the difficulties involved in applying geometry to design and creations. Have lots of extra blank paper on hand as it may require more than 1 attempt.

If you want this to be less challenging you can have the kids cut out the front and back sides and paste together.

But if you want to make this even more challenging, you can have them try to create this paper proof without any scissors, rulers, or straight edges. Using only origami folding and paper tearing methods to define the shapes and lines for the proof. This requires even more applied geometry to make the squares, triangles, lines, and diagonal folds. But it is so much harder to get them all to line up geometrically perfect on front and back with this Origami approach. So consider how much time you have and how challenging you want this to be before adding this Origami constraint to the design challenge.

Includes 6 Pages:
1) Cover
2) Background and Instructions
3-4) Relates visual examples to the math portion of the theorem
5) The final math portion of the proof.
6) Examples of lines, squares, triangles, needed to create the paper proof

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6 pages
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