The concept of similarity of figures on the Galilean plane

In Euclidean plane geometry, one of the important concepts is the similarity of figures. Similarity is defined as a one-to-one mapping of figures, where the distance between any two corresponding points is multiplied by a constant factor called the coefficient of similarity. In the geometry of the Galilean plane, the formula for calculating the distance between points is divided into two parts, with each pair of points corresponding to one of these parts. On the Galilean plane, the similarity of figures can be defined exactly as it is on the Euclidean plane. However, there are three additional ways to define the similarity of figures on the Galilean plane that have no analogs in Euclidean geometry.