Final answer:
Ivan the Great used evidence such as his defiance of Mongol rule, the rebuilding of the Kremlin, and the annexation of territories to prove his claim as the heir to the Roman and Byzantine emperors.
Step-by-step explanation:
As the ruler of the Grand Duchy of Moscow, Ivan the Great used several pieces of evidence to prove his claim as the heir to the Roman and Byzantine emperors. One important piece of evidence was Ivan's refusal to pay tribute to the Golden Horde, showing his defiance of Mongol rule and his desire for independence and sovereignty.
Additionally, Ivan's decision to rebuild the Kremlin in Moscow and declare his kingdom as the new Rome demonstrated his ambition to establish his own empire and connect it to the legacy of the Roman and Byzantine emperors.
Lastly, Ivan's annexation of territories such as Kazan, Astrakhan, and Siberia further solidified his claim to imperial power by expanding his realm and exerting control over lands once held by the Byzantine Empire.