A corollary is something that naturally follows from something else that's already been proven or established. Think of it as a bonus conclusion: once you've figured out one thing, a corollary is another truth that comes along almost automatically.

In mathematics, if you prove that all squares are rectangles, a corollary might be that squares must have four right angles (since rectangles do). You didn't set out to prove that second fact, but it flows directly from what you already showed.

The word works outside math too. If your school proves that students learn better when well-rested, a corollary might be that late-night video games can hurt test scores. If a scientist discovers that a certain plant needs very little water, a corollary is that it would grow well in deserts.

The key thing about corollaries is that they're not the main point you were trying to make. They're the natural, logical consequences that follow once you've established something bigger. When you understand one important truth, corollaries are the smaller truths that come tumbling out behind it, almost like they were waiting to be noticed.