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We all know that the Pythagorean Theorem states that a^2 + b^2 = c^2 in right-angled triangles in Euclidean geometry.

But you may have forgotten that the "squared" is meant literally here:
the square on side a (i.e. the area of that square) + the square on side b (i.e. the area of that square) = the square on side c, i.e. the area of that square.

QUESTION: can the theorem be generalized to shapes other than squares?

For example, what about **rhombus** on side a + **rhombus** on side b? Do the areas of the two rhombuses (rhombi?) equal
the area of the rhombus on side c? Find out. Does anything follow?

Obviously a **rectangle** as a shape is problematic because the possibilities are unlimited.
A key one is the special case of the square,
of course, but messing around with other rectangles with proportional relationships of width vs. length is interesting.

Investigate other areas of other shapes and their areas, regular and irregular.

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So, how general can we make the theorem?
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