How do you connect the ideas of congruency and rigid motion?

Rigid motion does not change the shape of an object. if you move an object to another place, you can think of it as a new object (a copy) at the new position and it will be congruent to the object at the original position. or, if two objects are congruent, you can move one object so it lies on top of the other, showing they are congruent.

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