The originality of Tolkien's works

[Thingol]

Recently I finished reading the epic poem Beowulf. When I read the scene where Beowulf fights the Dragon I was surprised to find quite a number of similarities between Smaug and the Dragon in Beowulf. For example the dragon is Beowulf is roused by a man who steals a jeweled cup from the dragon's hoard, just as Smaug is roused by Bilbo stealing a jeweled cup. In addition the description of the Dragon in Beowulf bears a striking similarity to the description of Smaug in The Hobbit. I asked my English teacher about this and he told me that it used to be common practice for authors to use the works of other authors in their writings. He said that the idea that something must be original to be considered good is purely a development of the last fifty years or so. Authors like Shakespeare, Milton, Melville, Byron, Chaucer, Dante, Dickens etc... all borrowed much of their writings from Greek mythology, the Bible and even from each other. It was not uncommon for authors to directly take passages from other authors and place them into their writings without even an acknowledgement. He went on to say that since Tolkien's writing style was closer to that of the 19th century and not of the 20th that I should not be surprised if I find out that Tolkien did a considerable amount of "borrowing" from other sources. I am curious if anyone has any ideas as to how original Tolkien's works actually are?