The statement that correctly represents the similarity between the two figures is:
quadrilateral ABCD ∼ quadrilateral EFGH
This notation indicates that quadrilateral ABCD is similar to quadrilateral EFGH.
Make sure the orientation of letters is consistent with the properties of similarity (like corresponding angles and side lengths being proportional). If ABCD and EFGH are related in such a way, the first option is the appropriate choice.