Which landmark project was completed during the presidency of Theodore Roosevelt?

The Panama Canal is the correct answer because it represents a significant achievement during Theodore Roosevelt's presidency. Roosevelt recognized the strategic importance of the canal for both military and commercial shipping, as it would dramatically shorten the travel distance between the Atlantic and Pacific Oceans.

His administration was instrumental in negotiating the lease of the canal zone from Panama, which had just gained independence from Colombia with support from the United States. The construction of the canal was a monumental engineering project that faced numerous challenges, including disease and difficult terrain, but ultimately it was completed in 1914, enhancing international trade and naval mobility.

The other projects mentioned, while significant in their own right, were not completed during Roosevelt's time in office. The Transcontinental Railroad was finished in 1869, long before his presidency. The Hoover Dam was constructed later, starting in 1931 and completed in 1936, and the Appalachian Trail was established as a hiking trail but was not completed in its entirety until much later. Thus, the Panama Canal stands out as a defining accomplishment of Theodore Roosevelt's administration.