How do dilations relate to similarity?
Dilation transforms one figure into another one, similar to original.
Dilation is a transformation of scaling that requires a center of scaling and a factor of scaling.
Similarity is a relationship between two figures when there is a special transformation that transforms one figure into another.
This transformation can include any combination of rotation, shift and dilation.
That's why a pair of a source and its image after dilation are similar, but not all similar figures can be connected by dilation. For instance, rotation and/or shift transform a figure into another, similar one to the original, but not related through dilation..