To determine which statement best identifies a similarity between the territories controlled by the Byzantine Empire under Justinian I and the Roman Empire under Trajan, we can analyze the options provided.
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Neither empire controlled the entire Mediterranean coastline. - This is likely true for both empires, as neither had dominance over every coastal region along the Mediterranean.
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Neither empire controlled the entire Iberian Peninsula. - This is also true for both empires, as both had territories that did not encompass the whole peninsula.
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Both empires controlled Mesopotamia and the Italian Peninsula. - This is incorrect as while most of the Roman Empire included parts of Mesopotamia, control fluctuated, and Justinian I's territory was primarily focused on the Mediterranean and parts of North Africa, not all of Mesopotamia.
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Both empires controlled Asia Minor and the Italian Peninsula. - This statement holds true, as both empires did control Asia Minor and the Italian Peninsula during their respective eras.
Given this analysis, the best response that identifies a similarity is:
Both empires controlled Asia Minor and the Italian Peninsula.