Arigid transformation can also be referred to as an isometric transformation. the prefix "iso-" means "of the same" and "-metric" means "measure." how does the meaning of the word isometric relate to determining if an isometric transformation occurred?

As stated by the statement, isometric means same measure. So, when a rigid transformation occurs all the measures of the original figure (which will be transformed) will be the same of the new figure (the result of the transformation).

That means that you can verify that the transformation used was rigid by checking the measures of both (original and transformed) figures: if and only if the meausures of the final figure are the same of the original figure the transformation was rigid.