What rationale did the Supreme Court rely on in deciding that school segregation was permissible?

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The Supreme Court relied on the rationale that segregation in public facilities was not unconstitutional as long as the separate facilities were substantially equal. This was established in the landmark case Plessy v. Ferguson (1896), which allowed for separate but equal facilities based on race. However, this rationale was overturned in Brown v. Board of Education (1954), which declared that separate educational facilities were inherently unequal and violated the Equal Protection Clause of the 14th Amendment.

What Rationale Did the Supreme Court Rely on in Deciding