What does it mean to say that one square is "equal" to another? It probably seems reasonable to say that two squares are equal if they have sides of the same length. If two squares have equal areas, they will also have sides of the same length. But although "equal areas mean equal sides" is true for squares, it is not true for most geometric figures.

Consider the rectangles shown below. The areas of A and B and D are all 2 square units, but it is not reasonable to say that rectangle A "is equal to" rectangle D, although their areas are equal.

Geometry has a special mathematical language to describe some of these relationships. If Rectangle B is moved, turned on its side (rotation), and slid (translation), it would fit exactly in Rectangle A.

Two geometric figures are called congruent if...