There are many synonyms for the phrase "pertinent evidence," which is used to describe evidence that is relevant or applicable to a particular case or situation. Some synonyms for pertinent evidence include "relevant evidence," "material evidence," "admissible evidence," "probative evidence," and "significant evidence." Other possible synonyms include "key evidence," "crucial evidence," "important evidence," "useful evidence," "valid evidence," and "convincing evidence." Regardless of which synonym is used, the underlying implication is always the same -- the evidence is directly relevant to the issue at hand, and can help to support or undermine a particular position or argument.