If the congruence is direct, one object can be brought to coincide with the other by a convenient movement during which it behaves as a rigid body.

The movement may be:

a) a translation, when all the points of the object undergo an equal displacement in the same direction;

b) a rotation around an axis: all points on the axis will not change their position;

c) a rototranslation or screw axis, which may be considered as the combination of a rotation around the axis and a translation along the axial direction.

If the congruence is opposite, one object is said to be enantiomorph with respect to the other, and may be brought to coincidence by 5 operations:

1: an inversion, a symmetry operation with respect to a point;

2: a reflection, a symmetry operation with respect to a plane;

3: a rotoinversion, the product of a rotation around an axis by an inversion with respect to a point on the axis;

4: glide plane operation, the product of a reflection by a translation parallel to the reflection plane;

5: a rotoreflection, the product of a rotation by a reflection with respect to a plane perpendicular to the axis.