c. 1600, from Late Latin incongruentia "incongruity," from incongruentem (nominative incongruens) "incongruous, inconsistent," from in- "not" (see in- (1)) + congruens (see congruent). Related: Incongruency.
word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
early 15c., "suitable, proper, harmoniously joined or related," from Latin congruentem (nominative congruens) "agreeing, fit, suitable," present participle of congruere"agree, correspond with," literally "to come together," from assimilated form of com "with, together" (see con-) + a lost verb *gruere, *ruere "fall, rush," which de Vaan traces to a PIE *ghr(e)uho- "to rush in."
Geometry sense, "capable of being superposed," is attested by 1706. Related: Congruently.
<a href="https://www.etymonline.com/word/incongruence">Etymology of incongruence by etymonline</a>
Harper, D. (n.d.). Etymology of incongruence. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/incongruence