Final answer:
The Equal Protection Clause of the Fourteenth Amendment ensures everyone is treated equally under the law and does not permit guidelines that allow for racial segregation, as established by the overruling of Plessy v. Ferguson by Brown v. Board of Education.
Step-by-step explanation:
The Equal Protection Clause is a provision in the Fourteenth Amendment of the U.S. Constitution that mandates no state shall deny any person within its jurisdiction the equal protection of the laws. This clause is a critical tool used by the Supreme Court when evaluating state legislation. It ensures that individuals are treated equally under the law, and it forbids states from discriminating against people based on certain characteristics unless there is a valid reason to do so.
One guideline that is not used by the Supreme Court to apply the Equal Protection Clause is the allowance for racial segregation. The Court's ruling in Plessy v. Ferguson, which allowed for 'separate but equal' facilities, was later overturned by Brown v. Board of Education because it was determined that segregation did not align with the principles of equal protection.