Which sentence includes a nonrestrictive clause?

The sentence that includes a nonrestrictive clause is the one that provides additional, non-essential information about the subject while still allowing the sentence to maintain its main meaning without it. This is best illustrated in the correct choice, where the clause "which he built on a hill" adds information about the blue house but is not critical for identifying which blue house is being discussed. The main clause, "The blue house is quite large," still stands alone and makes complete sense without this additional detail. Nonrestrictive clauses are typically set off by commas, which signals that the reader can omit that part of the sentence without losing the primary meaning.

In contrast, the other sentences contain clauses that are important for identifying or specifying the subjects. For example, one of the options specifies "the blue house that he built on a hill," where the clause is essential to know which blue house is being referred to. Thus, it cannot be removed without changing the meaning of the sentence. Similarly, another option mentions "the student who won the prize," implying the identification of that specific student is crucial to the sentence. The distinction lies in whether the clause provides essential information (restrictive) or additional context (nonrestrictive).