Final answer:
The Supreme Court case that maintained the legality of segregation was Plessy v. Ferguson. It was later overturned by Brown v. Board of Education in 1954.
Step-by-step explanation:
The Supreme Court case that maintained the legality of segregation was Plessy v. Ferguson. This 1896 decision upheld the doctrine of "separate but equal," which allowed for racial segregation under the pretense that the separate facilities for blacks and whites were supposed to be of equal quality. The case of Plessy v. Ferguson established a legal basis for segregation until it was eventually overturned by Brown v. Board of Education in 1954, which ruled that separate educational facilities are inherently unequal, thus making segregation in public schools unconstitutional.