The phrase "In a sense we have come to our nation's capital to cash a check" uses extended metaphor. In this context, the "check" symbolizes the unfulfilled promises of freedom and equality for African Americans, and the act of "cashing" it represents the demand for those rights to be recognized and realized.
"In a sense we have come to our nation's capital to cash a check." uses a
hyperbole
personification
extended simile
extended metaphor
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