Pythagorean Proof by Rearrangement

This sketch contains a classic Pythagorean Theorem proof. Copies of a right triangle are arranged to form two large squares that share many connections. Hints below the sketch.

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1. How do we know the picture shows two squares? (The red and blue bordered, adjacent squares; not the red, blue and purple squares.) Are they congruent? How do you know?

2. What is the area of one of the squares, by knowing its side length?

3. What is the area of each of the squares as a sum of the areas of the shapes it is subdivided into?

4. Why does the arrangement of the triangles make the three additional, smaller squares?

5. Does this constitute a proof or are there assumptions to address?

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John Golden, Created with GeoGebra