Why are isometric transformation a part of the similarity transformations?

Isometric transformations are a subset of similarity transformations because they preserve both shape and size, meaning that the distances between points remain unchanged. Similarity transformations, which include isometric transformations, preserve the shape but can also allow for changes in size through scaling. However, isometric transformations specifically maintain the original dimensions of geometric figures, ensuring that angles and relative proportions are conserved. Thus, while all isometric transformations are similarity transformations, not all similarity transformations are isometric.