Final answer:
The Rio Grande is the river that marks the border between Mexico and the United States, beginning in southern Colorado and stretching to the Gulf of Mexico. It was central to the territorial disputes that led to the Mexican-American War and is heavily regulated by dams, including the Hoover Dam.
Step-by-step explanation:
The river that forms the border between Mexico and the United States and has its headwaters beginning in southern Colorado is the Rio Grande.
The Rio Grande played a pivotal role in the history of the border between the two nations, as tensions arose in 1845 when the United States annexed Texas and claimed the river as the border, while Mexico held onto the long-established Nueces River as the boundary.
This contention was a part of the broader Mexican-American War, which resulted in the establishment of the Rio Grande as the international boundary. The Gadsden Purchase later clarified and finalized this border, particularly in Arizona's Mesilla Valley.
Today, the Rio Grande is not only a significant geographical landmark but also an important water source heavily regulated by a system of dams and canals, including the renowned Hoover Dam.