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If you study the picture of the two triangles you will see that both have the same dimensions, and that the bottom triangle is just a rearrangement of the exact same pieces from the top triangle. So the question is, where does the extra square in the bottom triangle come from?

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I have seen this before. The second triangle is not really a triangle, the slopes of the two smaller triangles don't line up. This difference is where the square went to, nothing was actually taken out.

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