A reader recently wrote:
To be honest, I was stumped. A quick check of Webster's Collegiate Dictionary didn't help clarify. So I ordered Garner's Modern American Usage, "the preeminent contemporary guide to effective use of the English language," as it bills itself on the dust jacket. It just came in the mail today.
The entry under incongruous notes, "For the distinction between congruous and congruent, see congruent." Hmm. Flipping to that entry, I read, "these words are largely synonymous--meaning 'in agreement or harmony; appropriate'."
It turns out that incongruous ("not in harmony; unfitting") is "far more common" than congruous. Garner gives the example of "tinkling calls, so incongruous from such gigantic birds."
According to Webster's, incongruent is used in mathematics, such as incongruent triangles.
That said, I believe incongruous and incongruent are synonymous. I've seen them used interchangeably. It comes down to author preference, though incongruous seems to be more commonly used.
I'm not sure if my dear reader will be satisfied with this explanation. But I'm very satisfied to have Garner's Modern American Usage now on my bookshelf.
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