Common Core Standards: Math
2. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
If George Weasley were to run through a doorway leaving a George-shaped hole, Fred could waltz into this hole and he'd be a perfect fit in every way. That's what's called being congruent. Students should understand congruence as being identical—where all corresponding angles and sides are exactly the same.
Sometimes, it's not easy to tell if two shapes are congruent. If one twin lies down and the other stands upright, they might not look exactly identical. All we have to do to verify that they are congruent is have the both of them either standing up or lying down (which is difficult to do when they're both set on proving how different they are from one another).
Students should know that this happens to shapes, too. Sometimes, we have to pick them up, turn them, flip them, and move them around to see that they are actually congruent. If they are, then the only movements—or transformations—we need to perform are translation, reflection, or rotation.
Being familiar with the three congruence transformations is a good start, but students should know be able to describe which transformations are necessary to see the congruence between two figures as well as identify when two shapes aren't congruent.