Are either of those shapes actually triangles? Look carefully at the intersection of the diagonal with the grid. Or calculate the slopes of the diagonal lines.
There is a contradiction here, therefore there is something fishy going on, and I think it has to do with the assumption that the apparent triangles are truly triangles.
The four shapes do not come together to make a triangle. The small triangle (dark green) is a right triangle with legs 2 and 5; the large triangle (red) is a right triangle with legs 3 and 8. They are not congruent.
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