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On the internet I can find examples of both forms: "This triangle is congruent {to/with} that triangle", "this conclusion is congruent {to/with} the evidence".

Is there a correct form?

I'm specifically referring to the mathematical use of the word ("superposable so as to be coincident throughout", basically "the same shape and size") , but I assume the answer would apply for general use as well.

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  • In my experience, two triangles are congruent. One triangle isn't congruent around/about/above another triangle. The whole set is congruent. I haven't done research to support this as an answer.
    – jejorda2
    Dec 21, 2016 at 13:56
  • I think there's enough research shown in the question (now). Can it be unmark as "closed"?
    – Kumāra Bhikkhu
    Mar 13, 2019 at 11:39

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In mathematics, this adjective can be used in phrases like "A and B are congruent", "A is congruent to B", and, less commonly, "A is congruent with B".

Wiktionary confirms the usage I am accustomed to: congruence is an equivalence relation, so the usage would be analogous to "equivalent (to)" (or "isomorphic (to)").

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Ngram shows "with" is the more common expression used with congruent.

Congruent to is used in mathematics meaning:

  • having the difference divisible by a given modulus:

    • 12 is congruent to 2 (modulo 5) since 12−2=2·5

or geometry, (of figures) identical in form; coinciding exactly when superimposed:

  • ‘Each vertex triangle in the new hexagon is either congruent to one in the original hexagon or has the same base and height.’

(M-W, ODO)

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