On the contrary, it is quite possible to fix sixteen right triangles into one big triangle. In fact, all the triangles can be isosceles and congruent. Place one triangle in a "row." Then, place three triangles in a row lower than the first one, creating a trapezoid. Repeat with rows of five and seven triangles. This works because 1 + 3 + 5 + 7 = 4^2 = 16.
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