Informally, a Euclidean plane isometry is any way of transforming the plane without "deforming" it. For example, suppose that the Euclidean plane is represented by a sheet of transparent plastic sitting on a desk. Examples of isometries include:
* Shifting the sheet one inch to the right.
* Rotating the sheet by ten degrees around some marked point (which remains motionless).
* Turning the sheet over to look at it from behind. Notice that if a picture is drawn on one side of the sheet, then after turning the sheet over, we see the mirror image of the picture.
These are examples of translations, rotations, and reflections respectively. There is one further type of isometry, called a glide reflection (see below under classification of Euclidean plane isometries).
However, folding, cutting, or melting the sheet are not considered isometries. Neither are less drastic alterations like bending, stretching, or twisting.