In the sentence "The blue house that he built on a hill is quite large," what type of phrase is "that he built on a hill"?

In the sentence "The blue house that he built on a hill is quite large," the phrase "that he built on a hill" functions as a restrictive clause. A restrictive clause provides essential information about the noun it modifies—in this case, "the blue house." This clause specifies which blue house is being discussed, indicating that there may be multiple blue houses, but only one that he built on a hill.

If the clause were removed, the meaning of the sentence would change significantly, leading to potential confusion about which house is being referenced. This demonstrates the integral role the clause plays in identifying the subject.

In contrast, a nonrestrictive clause would provide additional, non-essential information and would be set off by commas. Descriptive and clarifying phrases could also convey information but do not specifically indicate the critical nature of identification that the restrictive clause does in this context.