Pythagorean Data

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a. Look at your right triangle examples on this triangle. How do you think ancient mathematicians noticed this cool pattern with the squares?

b. Check your other examples on this sketch. For each, record whether the sum of the areas of the smaller squares is <, =, or > the area of the large square.

c. What pattern(s) do you notice?

d. Why do you think your pattern(s) might be true?

John Golden, Created with GeoGebra