The statement that provides the most accurate investigation of why Ethiopia and Egypt have run into conflict over resource management is:
"Ethiopia's building of a dam on the Nile could impact Egypt's use of the Nile because they lie downriver."
This statement highlights the key issue in the conflict, which revolves around the management of the Nile River's water resources. The Grand Ethiopian Renaissance Dam (GERD) has been a significant point of contention, as Egypt, being downstream, is concerned about its access to water from the Nile, which is crucial for its agriculture and water supply.