In The Square Triangle, U.S. Marshal Matt Dillon patrols the tumultuous streets of Dodge City, where lawlessness often reigns. The episode opens with Dillon reflecting on the nature of his job, underscoring the loneliness and vigilance required of a lawman. The arrival of Eva Morley, a striking woman with a complicated past, stirs the pot of local tensions. Her beauty and charm draw the attention of several men, including her husband, Al Morley, and a young cattle buyer named Red Lawson.