Final answer:
The correct preposition to complete the sentence is 'with,' indicating an ongoing communication between two parties.
Step-by-step explanation:
The correct preposition to use in the sentence 'I correspond _______ her regularly' is with. So, the complete sentence should be: 'I correspond with her regularly.'
The preposition 'with' is used to indicate that two or more people are doing something together or are involved in something at the same time. In the case of corresponding, it suggests an exchange of communication between two parties.
The correct preposition to fill in the blank is With. Therefore, the statement should read as follows: I correspond with her regularly.