congruently

Congruently is an English adverb derived from the adjective congruent. It denotes performing or describing something in a manner that is congruent—in agreement with a rule, standard, pattern, or relation. In mathematics, congruently often emphasizes that a process preserves a specific congruence or the properties of objects that are congruent.

In geometry, congruence refers to two figures having the same shape and size, so that one can be transformed into the other by a rigid motion (such as a translation, rotation, or reflection). When objects are described as congruently arranged or congruently positioned, it usually means they have been placed in a way that preserves their congruence with each other, enabling a perfect match if overlaid.

Beyond geometry, congruently is used in a broader, more formal sense to describe agreement with evidence, standards, or expectations. For example, a result or interpretation may be said to be congruently aligned with prior data or with theoretical predictions.

Etymology: the word comes from the Latin congruentia, from congruere “to agree, fit together,” itself from con- “together” and the root associated with grip or coming together.

Usage notes: congruently is relatively rare outside technical writing. In everyday language, speakers often use congruent as the primary adjective and reserve congruently for contexts involving explicit alignment with a rule, pattern, or congruence relation.

See also: congruent, congruence, congruence relation, rigid motion, modular arithmetic.