gru

The root gru comes from Latin congruere, formed from con- ("together") and an old verb gruere whose core image is things running or coming together until they meet. Picture two streams flowing toward each other and joining, or two edges sliding together until they touch all along their length. That physical meeting — coinciding perfectly — is the seed of the whole family.

From "meeting and coinciding" came the abstract sense of matching and agreeing. If two things meet so cleanly that they line up everywhere, they are in accord.

The family is built almost entirely from suffixes on this one stem:

- congruent (con- + gru + -ent) = "coming together / fitting." In everyday use it means in agreement, consistent (a strategy congruent with our values). In geometry it has a precise sense: two figures are congruent when they have exactly the same shape and size — they would coincide perfectly if laid on top of each other. That geometry meaning is the literal Latin image preserved intact.
- congruity (con- + gru + -ity) = the state of fitting together: harmony, consistency, appropriateness.
- congruous (con- + gru + -ous) = fitting, suitable, in accord — rarer than congruent, mostly literary.

Then the prefix in- ("not") flips the whole branch into mismatch, and this negative side is actually the more common one in modern English:

- incongruous (in- + congruous) = out of place, clashing, not fitting the surroundings — a clown at a funeral, a skyscraper among cottages. This is the everyday workhorse of the family.
- incongruity (in- + congruity) = the noun: a mismatch, a jarring inconsistency, or the quality of being out of place.
- incongruent (in- + congruent) = not matching / not consistent, used in formal or technical writing (and as the negation of geometric congruence).

One more relative lives mostly in mathematics: congruence, the state of agreeing, and in number theory the relation of two numbers leaving the same remainder ("congruent modulo n"). Same root, same idea of coinciding.

The takeaway: gru is about two things lining up so well they meet. Add con- and they agree; add in- and they clash. The geometric "same shape and size" meaning of congruent is not a coincidence — it is the original Latin picture of two things laid one on the other and coinciding exactly.