In terms of classical rhetoric, King's speech adheres quite closely to the usual structure and argumentative strategies found therein, as the other two answers have described.
The part of King's speech most everyone remembers is his use of peroratio, the concluding portion of the speech. In classical rhetoric, peroratio is the speaker's way of ending on an emotional note. This does not equal cheap pathos or sentimentality, but a meaningful use of emotional appeal that relates to the arguments previously put forth by the speaker. King does this during the last section of this speech, where he repeats the phrase "I have a dream" and describes his idea of how the American Dream will only truly come to fruition when those of every race coexist in respect and equality. The imagery he uses is emotionally charged, evoking innocence above all (images of children of all races joining hands in harmony).
In this section, King continues to also appeal to religious ideas, referencing the Psalms and the...
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