I don't remember the definition of "congruent". I graduated with honors in Computer Science, and took many math classes along the way and did very well, and the topic of "congruency" never came up beyond high school mathematics.
There's definitely something weird going on here. I imagine that it will be tempting for people on Hacker News to argue that they know the definition of "congruent" and it's not a difficult question and I should turn in my degree, but whatever.
Also, when we did the "congruent triangles" stuff in school, it was actually the most "graphical" way of conducting mathematical proofs. It was a very fun way to practice doing proofs. I don't even remember how much we continued to prove stuff in other parts of math. And again I think knowing about conducting proofs is useful/essential for CS.
Could it be that you never had the congruent stuff at school? Our teachers mentioned that there are alternative ways to do geometrical proofs (I think with mirroring and projections?), so your teacher might have chosen another route. Because the congruency stuff is really easy to remember imho, it seems likely you never actually heard about it.
Summary of "the congruency stuff" off the top of my head: two triangles are congruent if the have either three equal edges, or two equal edges with an equal angle between them, or one equal edge and two equal angles. (equal meaning same length for edges). I think that's it :-/ (it's late...).
If we rely on the average state of mind of a population to guide education, we will quickly end up teaching nothing. We should instead strive to teach as much as possible with the understanding that some information will be forgotten. We don't want our children to be as good as us. We want them to be better than us.