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Today I was made aware of the term "congruency" as a word related to congruence in the same way that equality is related to equation. I have never seen the term "congruency" used in math before, and a web search suggests that when "congruency" occurs in math it is only in the context of congruent triangles in plane geometry; I have never seen it used in the context of congruences in modular arithmetic.

If you have encountered the term "congruency" before in a math book, do you consider this term common or rare? I suspect even in geometry this term is not often used, but I would not consider myself any kind of expert on the terminology used in high school geometry courses.

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    $\begingroup$ It seems to me that "congruency" would be used whenever "congruent" is used and the grammatical aspects of that use warrant the use, and the infrequency of its use is primarily due to the infrequency of the grammatical reasons for using it. That is, I don't consider "congruency" as a different term, but rather a grammatically different version (in the same way that "similar triangles" and "similarity relation" are). That said, maybe this google books search for "congruency" + "number theory" will be of interest. $\endgroup$
    – Dave L Renfro
    Commented May 5, 2023 at 20:10
  • $\begingroup$ Never encountered, myself... But, sure, "transformational grammar" can easily (subliminally) generate non-standard forms... Still, again, no, I've never used that form myself, and never seen it, till this post. $\endgroup$
    – paul garrett
    Commented May 5, 2023 at 21:45
  • $\begingroup$ For all of the ways I can think that I might use “congruency,” I would just use “congruence” instead. Could you give an example of how you've seen it used? $\endgroup$
    – Ben Jones
    Commented May 6, 2023 at 3:39
  • $\begingroup$ @BenJones I agree with you: I’ve never seen that term in real use. I saw it in a message someone wrote to me who thought they had been taught it (in school?). Do a Google search. You’ll see results related to triangle congruences. $\endgroup$
    – KCd
    Commented May 6, 2023 at 5:13
  • $\begingroup$ The term congruency is sometimes used interchangeably with the term congruence in the UK, and I've seen it in secondary school textbooks in relation to geometry. Perhaps it is less common in the US? $\endgroup$
    – A. Goodier
    Commented May 6, 2023 at 10:32

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