Congruence (manifolds)

Congruence in mathematics is like matching shapes on a piece of paper. Imagine you have two pieces of paper with the same shape drawn on them. They might not be in the same place or facing the same way, but they look exactly the same. That means they are congruent.

Now, imagine the piece of paper is actually a special kind of shape called a manifold. Manifolds are like shapes that can bend and twist without breaking. Congruent manifolds are like two manifolds that can bend and twist in the same way and still look the same.

Think about it like this: If you have a long piece of paper, and you bend it like a rainbow, it looks different than if you bend it like a U. But if you have two pieces of paper that are congruent, you can bend them both into rainbows or Us, and they will still look the same as each other.

So in summary, congruence in manifolds means that two shapes that can bend and twist without breaking are considered the same if they can be bent and twisted in the same way to look exactly alike.