Pythagorean Card Table

This card table approximates a well-known proof of the Pythagorean Theorem.

Here we add some lines (not quite accurately, but it’s an approximation!):

We have four right triangles,each with sides a and b, and hypotenuse c. The area of the table is \( {{c}^{2}}\). To get the Pythagorean theorem, find the area of the table in another way — by adding the areas of the small square in the middle and the four right triangles (I’ll let you figure out that step yourself). Set the terms equal, and you should have \( {{c}^{2}}={{a}^{2}}+{{b}^{2}}\)

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