Final answer:
In 1821, the significant events included the signing of the Adams-Onís Treaty between the U.S. and Spain, and pivotal Supreme Court decisions in Dartmouth College v. Woodward and McCulloch v. Maryland cases.
Step-by-step explanation:
The two most significant events that happened in 1821 would likely be the signing of the Adams-Onís Treaty and the decisions made in two important United States Supreme Court cases: Dartmouth College v. Woodward and McCulloch v. Maryland.
The Adams-Onís Treaty, signed by the United States and Spain, ceded Florida to the U.S. and defined the boundary between the U.S. and New Spain.
On the other hand, the landmark Supreme Court cases solidified the power of the federal government with McCulloch v. Maryland affirming the doctrine of implied powers of the federal government and Dartmouth College v. Woodward establishing a precedent for the sanctity of contracts against state interference.