Answer:
1). A painting <u>belonging</u> to the Queen has been stolen.
2). These beautiful costumes, <u>worn</u> by famous opera singers are for sale.
3). The star of the show is an actor <u>known</u> by most people as a TV presenter.
4). It was difficult for people <u>sitting</u> at the back of the theatre to hear all the words.
5). I bought a copy of the novel <u>signed</u> by the author.
6). This piece, <u>written</u> by my piano teacher, is one of my favorites.
7). The fast train,<u> leaving</u> in five minutes, will get you to London in less than an hour.
Explanation:
Participle clauses are defined as the clauses beginning with either present(walking, going, etc.), past(read, reached, etc.), or perfect participle(having gone, having done, etc.). It primarily functions to help convey the information in a more brief and precise manner. It functions to provide detail to the sentence either by modifying the verb or a noun/pronoun.