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Which word, incongruous or incongruent, is correct in the following sentence:

That statement was indisputably ___________ with the definition of a shy man.
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I don't like either one here, but I believe "incongruent" is the better choice.

Your statement really lacks the necessary parallelism. A is incongruent with B.

I think in terms of geometry, where we compare two similar things: "The two triangles are incongruent." Triangle A B C is incongruent with triangle D E F.

I'd use "incongruous" to say that something is out of place (or, doesn't fit) in a particular situation, or configuration. "Her appearance - wearing a formal gown to the church social, and then getting plastered - was completely incongruous."

We have to assume that in your example, the "statement" is supposedto be "the definition of a shy man" - something of a stretch.Emotion: nodding

Edit. Well, I suppose you're covered either way. My Am. Htg. gives a second definition for "incongruent" as "incongruous."
It also gives a second definition for "incongruous" as made up of disparate, inharmonious (discordant) parts. That is, the parts are parallel, but not in agreement. I'd save that sense for "incongruent." What do I know??Emotion: thinking
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Maybe "incongruent" is the proper word for your sentence. I found a somewhat similar sentence in THE NEW OXFORD AMERICAN DICTIONARY: "The rules may NOT be CONGRUENT with the requirements of the law." PLEASE let us know if you discover the "correct" answer from another source.
Don't know how I forgot to mention that my first thought was that the preposition "with" is a key in this particular case, as is born out in your quote. I don't hear (in)congruous with - although the dictionary definitions seem to allow it.
"Incongruous" is definitely the more popular term in general use.

Incongruent

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Incongruent