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

 Messages: [ Previous | Next ]
 Walter Whiteley Posts: 146 Registered: 12/3/04
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.

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

>
> what does conguent mean?
>

Date Subject Author
5/24/00 avanti gabourel
5/24/00 Walter Whiteley
5/27/00 John Conway
12/30/04 Glen Woodburn
5/24/00 Guy Brandenburg