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Texas as a Republic (1836-1845)
Republic of Texas flag.

Ten years of independence brought the Texas Republic epidemics, financial crises and continued clashes with Mexico. But enduring Texas imagery was born in this period: the American cowboy; Texas Rangers with their Colt six-shooters; the rugged individualism of Sam Houston. On December 29, 1845, Texas joined the United States. The red, white and blue flag with its lone star adopted by the Republic in 1839 became the state flag.

Source: Lonestar Junction; Texas Handbook Online. (full source)