Final answer:
The laws that prohibited racial intermixing were known as anti-miscegenation laws, part of the Jim Crow system of segregation. These were abolished in 1967 with the Loving v. Virginia case.
Step-by-step explanation:
The laws that prohibited the mixing of racial groups through marriage, cohabitation, or sexual contact are known as anti-miscegenation laws. These laws, which criminalized interracial marriage and other forms of interracial relationships, were part of a larger system of racial segregation laws commonly referred to as Jim Crow laws.
The legal framework for segregation in the United States was enshrined by the Supreme Court's Plessy v. Ferguson ruling, which established the doctrine of "separate but equal". It wasn't until the landmark case of Loving v. Virginia in 1967 that the last of these anti-miscegenation laws were declared unconstitutional, allowing individuals to marry regardless of race.