WASHINGTON—The morning after the House voted along party lines to impeach President Trump, it was uncertain when and under what procedures the Senate would conduct his trial.

The House on Wednesday approved abuse-of-power and obstruction-of-Congress articles against Mr. Trump in the wake of his pressing Ukraine to investigate former Vice President Joe Biden, a leading 2020 Democratic presidential candidate. Nearly all Democrats, led by House Speaker Nancy Pelosi (D., Calif.), supported the charges, while the chamber’s Republicans…

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