Different kinds of writing require different proofs. A proof can take the form of an example, quotation, statistic or any other kind of specific evidence that proves a claim.
Personal or societal examples are acceptable for persuasive essays that don't require research. An expository essay or essay that requires research necessitates proofs from outside sources. In a literary essay, writers find proofs from the actual text they are analyzing. For example, writers could back up a claim that Hamlet only pretends insanity by quoting the famous line, "I am but mad north-north-west."
Following a format is not enough to guarantee an "A" on a paper. Successful essays contain logic -- that is, the connections between ideas make sense. They sound believable and realistic. They do not commit logical fallacies, such as making a straw man argument or jumping to conclusions. The logical soundness of a proof sentence is crucial to the credibility of the claim it supports. Proofs that are off-topic or actually disprove a claim a writer is trying to make weaken the persuasiveness of an essay overall.
Every body paragraph of an essay needs to contain proof sentences. Typically, every body paragraph should begin with a topic sentence that directs the ideas following. Effective paragraphs contain two or three supporting points, followed by a proof sentence for each point. For example, a standard paragraph follows the format of topic sentence-point-proof-explanation-point-proof-explanation-point-proof-explanation-concluding sentence. Of course, transitional words, phrases and sentences help create flow in this structure.
Effective essay writers smoothly integrate proof sentences that contain quotes into their own sentences. That means they incorporate the quote into their own sentence; leaving a quote in its own sentence creates a "floating" quote, which makes the essay sound disjointed. Writers face several options for integrating quotes. They can introduce quotes by indicating the person speaking or writing, as in "Hamlet declared, 'I am but mad north-north-west,'" or "The author states that 75 percent of persons surveyed 'would never lie to their spouse.'" Writers can also begin sentences with quotes or place them in the middle: "'I am but mad north-north-west,' declared Hamlet" or "When Hamlet declares that he is 'but mad north-north-west,' this demonstrates his insanity is a pretense."