Final answer:
Dr. Martin Luther King Jr. used the analogy of a bad check to highlight the unfulfilled promises of equality for African Americans, emphasizing the need for the U.S. to live up to its democratic ideals.
Step-by-step explanation:
Dr. Martin Luther King Jr. used various analogies in his I Have a Dream speech. One compelling part of his speech included the analogy of a bad check, where he compared America's promises of liberty and justice to African Americans to a promissory note that had come back marked 'insufficient funds.' This analogy related directly to the condition of people of color in 1964 by highlighting the unfulfilled promises of freedom and equality. In the broader context of civil rights, it amplified the urgent need for the United States to honor its democratic ideals by providing equal rights and opportunities to all its citizens regardless of race.