Politics always involves a measure of performance. And on that score, few moments rival the one on Wednesday morning at the White House, when President Biden and President-elect Donald J. Trump pretended in public to like and respect each other — for a total of 29 seconds.

They shook hands despite years of animus and recriminations. Mr. Trump has called Mr. Biden “crooked” and a “communist,” and has vowed to investigate his actions in office. Mr. Biden has said Mr. Trump is a “dictator” who tried to steal an election and would “sacrifice our democracy” in his pursuit of power.

On Wednesday, at least, the nation’s 46th president was determined to uphold the traditions that have long surrounded a peaceful transfer of power — offering to do “everything we can to make sure you’re accommodated, have what you need” — even if they were traditions that Mr. Trump refused to extend to him four years earlier.

Mr. Trump responded as they posed in front of a roaring fireplace in the Oval Office: “I appreciate very much a transition that’s so smooth, it’ll be as smooth as you can get.”

Up until less than two weeks ago, the president-elect regularly derided Mr. Biden as weak, infirm and demented. On Wednesday, he referred to the president merely as “Joe,” offering his appreciation for the gracious hospitality.

It was a remarkable half minute, followed by a closed-door meeting of the two men, along with their chiefs of staff, that lasted almost two hours. But beneath the public disguise, both men were dealing with starkly different realities.