In the sentence, "The books on that shelf are mine.", is the prepositional phrase an adjectival phrase or an adverbial phrase?

Adverbial phrase :)

Explanation:

Have a nice day and everyone else looking at it too!

Hope I could help! :)

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quite an interesting way to teach topic sentences, because the answer to this question is the best definition of a topic sentence that one can present, it is as if answering the questions taught you how to do it, this is some real teaching, it is terribly well-done.

the topic sentence in this paragraph is:

topic sentences writers stay on track and keep a paragraph from becoming an aimless collection of sentences about an idea.

which incidentally tells you what a topic sentence should be.