In
geometry, two figures or objects are congruent if they have the same
shape and size, or if one has the same shape and size as the mirror image of the other. More formally, two sets of
points are called
congruent if, and only if, one can be transformed into the other by an
isometry, i.e., a combination of
rigid motions, namely a
translation, a
rotation, and a
reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. So two distinct plane figures on a piece of paper are congruent if we can cut them out and then match them up completely. Turning the paper over is permitted.