Use the meanings of the prefixes sur- and dis- to explain the difference between surmounted and dismounted.

The prefix 'dis' means apart, away; that is to move away from something while the prefix 'sur' means over, above.
To dismount means to get off something or to remove a thing from its support. For example: The king dismounted the horse majestically.
To surmount means to overcome a difficulty or an obstacle. For example: 
All the political differences between the two countries were surmounted. 

The United States went to war with Mexico in 1846. ... By the end of the war, Mexico would lose almost half its territory to the U.S., including lands from Texas to California. The war was a key event in American History as it fulfilled its 'manifest destiny', encompassing land from the Atlantic Ocean to the Pacific.

Explanation:

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