Final answer:
The Rump Parliament tried Charles I for treason due to a culmination of political and religious conflicts, leading up to the English Civil War, which saw the Parliamentarians triumph over the Royalists. His execution signified a historic shift in the balance of power between monarchy and Parliament.
Step-by-step explanation:
The Rump Parliament put Charles I on trial for treason because the relations between the king and the Parliament had been declining for several years, eventually leading to the English Civil War. Charles I was viewed as a proponent of absolute monarchy who had attempted to rule without Parliament, which strained fiscal resources and aggravated political tensions. His association with Catholic practices through his marriage and the religious reforms of his ally, Archbishop Laud, further alienated the Puritan majority in Parliament.
After the Parliamentarians, led by Oliver Cromwell's New Model Army, defeated the Royalists, Charles was captured, tried, and executed in 1649. This marked a historical moment, where a reigning monarch was tried and indicted by a legislative body, signifying a shift towards constitutionalism where Parliament held the power to challenge royal authority.