Final answer:
The Panama Canal was constructed as a result of the U.S. supporting Panama's independence from Colombia, following President Roosevelt's strategy to secure a route for the canal after Colombia rejected his initial proposals.
Step-by-step explanation:
The major construction project undertaken as a result of the U.S. helping a small Central American country to win their independence from Colombia was the Panama Canal. In the early 20th century, President Theodore Roosevelt facilitated Panama's independence from Colombia to ensure the United States could construct the canal.
The Colombian government initially rejected the terms proposed by the U.S., which led to Roosevelt's support of the Panamanian independence movement. After Panama gained its independence with the help of the United States' military intervention, a treaty was signed granting the U.S. the rights to build and operate the Panama Canal, which was completed in 1914.
This event occurred in the context of the U.S. seeking more influence and control over the region, often using military power to achieve strategic and economic aims, as seen with the later Alliance for Progress and actions such as the CIA involvement in Guatemala.