One witness said that Mr. Giuliani was representing Mr. Trump’s desires when he demanded that “Ukraine make a public statement announcing investigations of the 2016 election/DNC server and Burisma.”

Mr. Trump instructed officials to work with his personal lawyer Rudolph W. Giuliani on Ukraine matters. A new set of documents shows that Mr. Giuliani expressed to Mr. Zelensky that he was working with the president’s “knowledge and consent.”

In a July phone call , immediately after a discussion of military aid, Mr. Trump asked President Volodymyr Zelensky of Ukraine to “do us a favor” and pursue investigations that could give him personal political benefits.

It is widely accepted among scholars that an official does not need to commit an ordinary crime to be impeached.

Even if Mr. Trump did coerce the Ukrainians for his personal gain, his actions were not impeachable because the House did not accuse him of any violation of the law.

The White House blocked key witnesses who interacted directly with Mr. Trump from testifying to the House and refused to turn over internal documents.

Democrats have relied on the testimony of officials who largely do not have firsthand knowledge of what Mr. Trump himself was privately saying about the withholding of a White House meeting and military aid.

One witness testified that Mr. Sondland had told him the president had said that they would be at a “stalemate” if Mr. Zelensky did not make a public announcement.

Mr. Trump told Gordon D. Sondland, the ambassador to the European Union working on his behalf in Ukraine, that he wanted “no quid pro quo” from Mr. Zelensky.

While Mr. Trump did not mention any consequences for not fulfilling his request, officials testified that they came to believe that a foreign aid freeze and a delayed White House meeting were being tied to an announcement of investigations.

There was no explicit quid pro quo in the reconstructed transcript of the phone call, and Mr. Zelensky has said that he did not feel pressured by Mr. Trump.

While Mr. Trump did not mention any consequences for not fulfilling his request, officials testified that they came to believe that a foreign aid freeze and a delayed White House meeting were being tied to an announcement of investigations.

One witness testified that Mr. Sondland had told him the president had said that they would be at a “stalemate” if Mr. Zelensky did not make a public announcement.

The White House blocked key witnesses who interacted directly with Mr. Trump from testifying to the House and refused to turn over internal documents.

It is widely accepted among scholars that an official does not need to commit an ordinary crime to be impeached.