The prosecution and defence teams are each given two hours to deliver their positions before the lawmakers cast their votes on the articles of impeachment.
The Senate previously voted 51-49 to bar witness testimonies during the impeachment trial and thus it is scheduled to conclude with a final vote on Wednesday, 5 February.
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The House of Representatives, controlled by the Democrats, previously claimed that Trump had a "quid pro quo" with Zelensky; however, both presidents firmly denied the accusations.
Joe Biden has admitted in the past that as vice president, he threatened to withhold about $1 billion in US military aid to Kiev unless the Ukrainian government dismissed a prosecutor who was probing Burisma – a company that employed his son – over possible corruption.