Page "Euclidean space" Paragraph 4

One way to think of the Euclidean plane is as a set of points satisfying certain relationships, expressible in terms of distance and angle.

For example, there are two fundamental operations on the plane.

One is translation, which means a shifting of the plane so that every point is shifted in the same direction and by the same distance.

The other is rotation about a fixed point in the plane, in which every point in the plane turns about that fixed point through the same angle.

One of the basic tenets of Euclidean geometry is that two figures ( that is, subsets ) of the plane should be considered equivalent ( congruent ) if one can be transformed into the other by some sequence of translations, rotations and reflections.

( See Euclidean group.