Which was used to declare jim crow laws constitutional in the 1800s?

It was the Separate but Equal doctrine.

According to this doctrine, racial segregation did not violate the 14th Amendment of the U.S. Constitution which guaranteed ' equal protection' under the law to all people. This doctrine was confirmed in Plessy v. Ferguson Supreme Court decision of 1896, which allowed for state-sponsored segregation.

Jim Crow laws were state and local laws that enforced local segregation in the United States. Under Jim Crow, African Americans were relegated to the status of second class citizens. The 'separate but equal' policy was extended to public facilities, means of transport, schools, restaurants and restrooms. The facilities were, however, interior and underfunded compared to the facilities of white Americans.

i would go with the last one