The correct answer is the following.
The territorial boundaries of the United States in the 1800s correspond with moderns states borders after the territorial expansion that happened from 1790 to 1850.
Many members of the US government believed that the westward expansion was a necessity for the new nation to prosper. So in 1803, ordered the purchase of the Louisiana territory to the French. This action doubled the size of the country. Then, colonizers moved to the West to the Plains, where they encounter the logical resistance of the Native American Tribes that lived there, in what today is the territory of Oklahoma. The US government had to pass the Homestead Act of 1862 that gave 160 acres of land for people to work the land and make it productive. Another factor for the territorial expansion happened during the California Golden Rush from 1848 to 1855. That is how the territorial boundaries of the United States in the 1800s correspond with moderns states borders after the territorial expansion took place.