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Topic: What does congruent mean?
Replies: 4   Last Post: Dec 30, 2004 5:15 PM

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Walter Whiteley

Posts: 146
Registered: 12/3/04
Re: What does congruent mean?
Posted: May 24, 2000 7:20 PM
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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 half-turn 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 half-turn).

Walter Whiteley
York University

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> what does conguent mean?
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