A hypothetical for discussion: If the President is very unpopular. The House of Representatives and chooses to impeachment him/her because they don't like the hair style. They vote by clear majority for impeachment. Does the Senate have to hear the case?
The President is very unpopular with the Senate. They vote for removal because the Senate also does not like the hair style by more than a 2/3 majority.
Does the Congressional action remove the President from Office?
The President does not agree with the Congressional Action, can he challenge removal in court? Will the Courts hear his challenge?