Oedipus Rex is considered the most perfect of Greek tragedies and Sophocles the definitive Greek tragic playwright. How could I prove this is a...

First, there is an issue here with the passive voice. While you might claim that certain people have considered Oedipus Rex the most perfect of Greek tragedies and Sophocles the definitive Greek playwright, you could not prove that everyone who has ever written about the topic considers this to be the case, as it is not true. As is clearly shown by the evidence of Aristophanes' Frogs, opinions about the relative merits of different playwrights differed even in antiquity, and the Alexandrian canon includes three tragic playwrights.

The argument you can make is that Aristotle, in his Poetics, frequently mentions Oedipus Rex as a positive example, but he also mentions other tragedies, as in the statement: 

Now, the best tragedies are founded on the story of a few houses, on the fortunes of Alcmaeon, Oedipus, Orestes, Meleager, Thyestes, Telephus, and those others who have done or suffered something terrible.

You can certainly argue that Oedipus Rex has all the elements of a great tragedy outlined by Aristotle, including a noble hero who undergoes a reversal of fortune, an action of a certain magnitude, and the ability to evoke fear and pity. Thus it is easy to show that Oedipus Rex contains all the elements Aristotle considers essential to a great tragedy. However, not only did Sophocles himself write other plays containing these elements, but so did other playwrights. Thus "most perfect" would probably be an overstatement.

Oedipus Rex was considered a very important example of Greek drama in the Renaissance, but neoclassical critics felt that its construction was flawed. Among speakers of English, Richard Claverhouse Jebb, a nineteenth-century classicist was important in elevating the reputation of Sophocles in general and Oedipus Rex in particular.