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Oh but it is possible.

If you have a triangle with the three sides labeled 'a', 'b', and 'c' in clockwise order,

and you reassemble them in the clockwise order of 'a', 'c', 'b', then the new triangle

is not congruent to the original one. It's a different triangle.

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Q: Why isn't it possible to build a different triangle from anothers three line segments?
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A triangle is made from 3 joined line segments whereas a circle has no line segments around its circumference


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