Representative Jamie Raskin of Maryland, the lead impeachment manager, opened the trial’s formal arguments Tuesday afternoon with an explosive and deeply emotional appeal to senators as he made the case that they had every right to try a former president for official misconduct — and in fact were obliged to do so in the case of Donald J. Trump.

Mr. Raskin, a former constitutional law professor, opened his presentation with a joke about professors putting their students to sleep. But he went on to offer an argument that had senators sitting rapt in the Senate chamber, reliving the assault on the Capitol on Jan. 6 as he played a grueling and graphic video of the day and then laid out the constitutional reasons he said Mr. Trump must be tried.

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