# What preposition does "congruent" take? "Congruent to" or "congruent with"? [closed]

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.

• 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. Dec 21, 2016 at 13:56
• I think there's enough research shown in the question (now). Can it be unmark as "closed"? Mar 13, 2019 at 11:39

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)").

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)