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From Nordan Symposia
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[[File:lighterstill.jpg]][[File:Congruence_2008.jpg|right|frame]]
==Origin==
The [[Latin]] ''congruō'' [[meaning]] “I meet together, I [[agree]]”.
*[http://en.wikipedia.org/wiki/15th_century 15th Century]
==Definitions==
*1: the [[quality]] or state of [[agreeing]], coinciding, or being congruent
*2: a [[statement]] that two [[numbers]] or geometric figures are congruent
==Description==
'''Congruence''' (≅) is the state achieved by coming [[together]], the state of [[agreement]]. As an abstract term, congruence means similarity between objects. Congruence, as opposed to approximation, is a relation which implies a species of equivalence.
In [[geometry]], two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the [[mirror]] image of the other. More [[formally]], two sets of points are called congruent if, and only if, one can be [[transformed]] into the other by an [http://en.wikipedia.org/wiki/Isometry isometry], i.e., a combination of [[translations]], rotations and [[reflections]]. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. Two line segments are congruent if and only if they have the same length.
The related [[concept]] of [[similarity]] applies if the objects differ in size but not in shape.[http://en.wikipedia.org/wiki/Congruence_%28geometry%29]
[[Category: Mathematics]]
==Origin==
The [[Latin]] ''congruō'' [[meaning]] “I meet together, I [[agree]]”.
*[http://en.wikipedia.org/wiki/15th_century 15th Century]
==Definitions==
*1: the [[quality]] or state of [[agreeing]], coinciding, or being congruent
*2: a [[statement]] that two [[numbers]] or geometric figures are congruent
==Description==
'''Congruence''' (≅) is the state achieved by coming [[together]], the state of [[agreement]]. As an abstract term, congruence means similarity between objects. Congruence, as opposed to approximation, is a relation which implies a species of equivalence.
In [[geometry]], two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the [[mirror]] image of the other. More [[formally]], two sets of points are called congruent if, and only if, one can be [[transformed]] into the other by an [http://en.wikipedia.org/wiki/Isometry isometry], i.e., a combination of [[translations]], rotations and [[reflections]]. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. Two line segments are congruent if and only if they have the same length.
The related [[concept]] of [[similarity]] applies if the objects differ in size but not in shape.[http://en.wikipedia.org/wiki/Congruence_%28geometry%29]
[[Category: Mathematics]]
