Final answer:
The Supreme Court used the 14th Amendment to rule in favor of Chinese laundryman Lee Yick, emphasizing his right to equal protection under the law and due process.
Step-by-step explanation:
The Supreme Court cited the 14th Amendment in ruling that Chinese laundryman Lee Yick had been unfairly convicted. The 14th Amendment states that no state shall deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws. In this case, the Supreme Court ruled that the laws being applied to Lee Yick were not applied equally and thus violated the Equal Protection Clause, ensuring that all individuals, regardless of race, are treated equally under the law.