How do we know that Jesus fulfills the prophecies of the Old Testament?

Philip's response to the eunuch's question about the identity of the prophet in Isaiah 53 reveals that Jesus is the subject of these prophecies. In Isaiah 53, words like 'wounded for our transgressions' clearly point to Christ's sacrificial role for His people. According to Acts 8:35, Philip preached Christ from this Scripture, indicating that the entire Old Testament points to Jesus as the fulfillment of earlier promises. This demonstrates that understanding Jesus in the context of Old Testament prophecy is foundational to recognizing Him as the Messiah.