
n.
- Agreement, harmony, conformity, or correspondence.
- An instance of this: "What an extraordinary congruence of genius and era" (Rita Rack).
- Mathematics.
- The state of being congruent.
- A statement that two quantities are congruent.
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American Heritage Dictionary:
con·gru·ence |

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congruence |
noun
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congruence |
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Oxford Dictionary of Biochemistry:
congruence |
| conglycinin, conglutinin, conglutination | |
| coniferin, coniferyl alcohol, coniine |
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categories related to 'congruence' |

Rhymes:
congruence |
Wikipedia on Answers.com:
Congruence (geometry) |
In geometry, two figures are congruent if they have the same shape and size. This means that either object can be repositioned so as to coincide precisely with the other object. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of translations, rotations and reflections.
The related concept of similarity applies if the objects differ in size but not in shape.
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Contents
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In a Euclidean system, congruence is fundamental; it is the counterpart of equality for numbers. In analytic geometry, congruence may be defined intuitively thus: two mappings of figures onto one Cartesian coordinate system are congruent if and only if, for any two points in the first mapping, the Euclidean distance between them is equal to the Euclidean distance between the corresponding points in the second mapping.
A more formal definition: two subsets A and B of Euclidean space Rn are called congruent if there exists an isometry f : Rn → Rn (an element of the Euclidean group E(n)) with f(A) = B. Congruence is an equivalence relation.
Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size.
If triangle ABC is congruent to triangle DEF, the relationship can be written mathematically as:

In many cases it is sufficient to establish the equality of three corresponding parts and use one of the following results to deduce the congruence of the two triangles.
Sufficient evidence for congruence between two triangles in Euclidean space can be shown through the following comparisons:
The SSA condition (Side-Side-Angle) which specifies two sides and a non-included angle (also known as ASS, or Angle-Side-Side) does not by itself prove congruence. In order to show congruence, additional information is required such as the measure of the corresponding angles and in some cases the lengths of the two pairs of corresponding sides. There are a few possible cases:
If two triangles satisfy the SSA condition and the length of the side opposite the angle is greater than or equal to the length of the adjacent side, then the two triangles are congruent. The opposite side is sometimes longer when the corresponding angles are acute, but it is always longer when the corresponding angles are right or obtuse. Where the angle is a right angle, also known as the Hypotenuse-Leg (HL) postulate or the Right-angle-Hypotenuse-Side (RHS) condition, the third side can be calculated using the Pythagoras' Theorem thus allowing the SSS postulate to be applied.
If two triangles satisfy the SSA condition and the corresponding angles are acute and the length of the side opposite the angle is equal to the length of the adjacent side multiplied by the sine of the angle, then the two triangles are congruent.
If two triangles satisfy the SSA condition and the corresponding angles are acute and the length of the side opposite the angle is greater than the length of the adjacent side multiplied by the sine of the angle (but less than the length of the adjacent side), then the two triangles cannot be shown to be congruent. This is the ambiguous case and two different triangles can be formed from the given information, but further information distinguishing them can lead to a proof of congruence.
In Euclidean geometry, AAA (Angle-Angle-Angle) (or just AA, since in Euclidean geometry the angles of a triangle add up to 180°) does not provide information regarding the size of the two triangles and hence proves only similarity and not congruence in Euclidean space.
However, in spherical geometry and hyperbolic geometry (where the sum of the angles of a triangle varies with size) AAA is sufficient for congruence on a given curvature of surface.[2]
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Translations:
Congruence |
Dansk (Danish)
n. - overensstemmelse, kongruens
Nederlands (Dutch)
overeenstemming, congruentie
Français (French)
n. - concordance
Deutsch (German)
n. - Kongruenz, Übereinstimmung
Ελληνική (Greek)
n. - αναλογία, αντιστοιχία, (μαθημ.) ισότητα
Italiano (Italian)
congruenza, compatibilità, corrispondenza
Português (Portuguese)
n. - congruência (f), congruência (f) (Mat.), harmonia (f)
Русский (Russian)
согласованность, конгруэнтность
Español (Spanish)
n. - congruencia
Svenska (Swedish)
n. - inbördes överensstämmelse, kongruens
中文(简体)(Chinese (Simplified))
适合, 相合性, 一致
中文(繁體)(Chinese (Traditional))
n. - 適合, 相合性, 一致
日本語 (Japanese)
n. - 調和, 一致, 合同
العربيه (Arabic)
(الاسم) تطابق, موافقه, مطابقه
עברית (Hebrew)
n. - התאמה, חפיפות
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