There are different ways to express the phrase "k the same prize" using synonyms. One could say "win the equal reward," "obtain an equivalent prize," or "take home an identical award." Other options include "earn the matching trophy," "secure the corresponding honor," or "achieve the commensurate accolade." Essentially, all of these synonyms convey the idea that someone is receiving the same or an equivalent recognition as others in a given competition or event, whether it be in sports, academics, or the arts. Varying the phrasing in this way can add nuance and interest to one's writing, while still conveying a clear and precise meaning.