Final answer:
The prefix 'dia-' means 'through' or 'across,' as seen in words like 'diagonal' and 'dialogue' where it implies a passing through or a going across.
Step-by-step explanation:
The prefix dia- means through or across. It is one of many Greek and Latin prefixes that English has adopted into its lexicon. When attached to a word, dia- implies that there is a passing through or a going across of something. For example, diagonal is a line or plane that passes through a figure from one corner to another. Another example is dialogue, which is an exchange of ideas or conversation between two or more people, metaphorically crossing back and forth between participants.