After the united states defeated mexico at war, what happened to almost half of the mexican territory?

Almost half of all Mexican territory was given to the United States as a result of the Mexican-American War. The Mexican-American War officially ended with the Treaty of Guadalupe Hidalgo. In this treaty, Mexico agreed to giving up a significant portion of their land (known as the Mexican Cession). This portion of land contained many states that the US has today including: California, Arizona, New Mexico, Utah, and Colorado.

Essentially, anything west of the Rio Grande became part of the United States.

The answer is william henry harrison pursued and defeated british forces retreating into canada.