Final answer:
In Brown v. Board of Education of Topeka (1954), the Supreme Court based its decision on the Equal Protection Clause of the Fourteenth Amendment, ruling that segregated public schools are unconstitutional.
Step-by-step explanation:
In the landmark case Brown v. Board of Education of Topeka (1954), the U.S. Supreme Court ruled that racial segregation in public schools violated the Equal Protection Clause of the Fourteenth Amendment. This decision overturned the precedent set by Plessy v. Ferguson and declared that 'separate but equal' facilities, including schools, were inherently unequal. The Court recognized that segregated schools enforced a stigma of inferiority amongst African American students and concluded that segregation was unconstitutional, thus mandating the desegregation of public schools across the United States.
The Supreme Court relied most heavily on the equal protection clause of the Fourteenth Amendment to reach the decision in Brown v. Board of Education of Topeka (1954). The Court argued that racially segregated schools violated this clause as they created an inherently unequal education system based solely on race. By declaring separate educational facilities to be inherently unequal, the Court effectively overturned the 'separate but equal' doctrine established by Plessy v. Ferguson.