How the US Acquired California and New Mexico

Both territories entered the US through the Mexican–American War (1846–1848) and its aftermath.

War triggered by Texas annexation dispute and border tensions
US forces captured Monterey, San Francisco, Los Angeles (1846–1847)
Treaty of Guadalupe Hidalgo (1848) ceded California, Nevada, Utah, most of Arizona, plus parts of Colorado, New Mexico, Wyoming

Same war; US occupied Santa Fe (1846) without resistance
Guadalupe Hidalgo set border at Rio Grande—New Mexico became US territory
Gadsden Purchase (1853) added southern Arizona/southwestern New Mexico for $10M—securing southern transcontinental railroad route

Mexico lost ~55% of its prewar territory. The acquisitions completed the continental US (except Alaska, 1867; Hawaii, 1898).

Mexico