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Re: What does congruent mean?
Posted:
May 24, 2000 7:20 PM


I don't have my book on the origns of math words, but I believe the root meaning is 'throw together'. To me, in geometry, it means I can take isometries and place one object on top of the other: two congruent triangles, two congruent angles etc.
I very much follow the idea that geometry is about transformations and it is valuable to not only know that there IS a transformation taking one to the other, but often valuable to KNOW which.
Consider a parallelogram  with opposite sides equal. Drawing a diagonal, you find that the two sides are 'congruent'. Which transformation? A half turn about the mid point of the diagonal! In fact ALL of the essential properties of a parallelogram follow from the fact that there is a halfturn symmetry around this mid point (where the two diagonals meet). This includes the fact that opposite sides are parallel (don't meet).
A nice thing about all this is it works perfectly well on the sphere (except, of course, that the opposite sides do meet  at antipodal points equally spaced from the 'center' of the halfturn).
Walter Whiteley York University
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