The best response that identifies the relationship between the words "boisterous" and "obnoxious" is:
They are synonyms; their meanings are nearly the same.
While "boisterous" generally refers to loud, energetic, and cheerful behavior, and "obnoxious" typically describes behavior that is offensive or unpleasant, they can overlap in context when boisterousness is perceived as excessive or annoying. Hence, they are not identical in meaning, but have similar connotations in certain contexts.