They are trying a case presented to them. That's correct, and like a judge in our legal system, they rule on what has been presented. This isn't the Nepolianic system where the judge asks questions, calls new witnesses, etc., it's the US legal system wherein the judge rules on the case
as presented not as the judge can shape it with new witnesses or documents, further investigation, slide shows of what Mitt Romney did on his vacation when they visited a Chocolate milk production line, or anything else.
They judge the case as presented, they do not build both sides of a case. The trial consists of what was presented, not what they create.
... it's the US legal system wherein the judge rules on the case as presented not as the judge can shape it with new witnesses or documents...But the Constitution says 'try', not 'judge', and in our system a trial is both presentation of evidence, including new evidence, as well as a verdict.