Which battle resulted in the Sioux tribe defeating General Custer and his men?

The Battle of Little Bighorn, famously known as Custer's Last Stand, occurred on June 25-26, 1876, and was a significant conflict between the United States Army and the Lakota Sioux, along with their Cheyenne allies. In this battle, General George Armstrong Custer and his forces engaged a larger coalition of Native American tribes who were resisting U.S. encroachment on their lands as part of the broader context of westward expansion.

The Sioux's victory at Little Bighorn was pivotal, as it not only demonstrated their military capability but also underscored the growing tensions and conflicts between Indigenous peoples and the U.S. government. This battle became a symbol of Native American resistance against U.S. governmental policies aimed at their removal and assimilation.

The other options, such as the battles of Gettysburg and Antietam, are key battles in the Civil War, while Saratoga is known for being a decisive victory for the American colonial forces during the Revolutionary War. None of these battles are related to the conflicts between the Sioux and Custer, making the Battle of Little Bighorn the only relevant and correct answer in the context of the question.