Prosecutors say Reaves followed Curtis from NCCU in Durham to Raleigh, forcing her to pull over along I-540 and then repeatedly slashed and stabbed her with a knife. Her body was discovered by drivers passing on the highway January 30, 2008.
Reaves, who was a minister at Cedar International Fellowship in Durham, is charged with first-degree murder. If convicted, he faces life in prison.
Closing arguments are scheduled for Wednesday morning.