Final answer:
Beowulf convinces Hrothgar of his worthiness through his words and actions, assuring Hrothgar that he is not afraid of the dangers that Hrothgar has faced and showing his loyalty and commitment to protecting Hrothgar's people.
Step-by-step explanation:
Beowulf tries to convince Hrothgar of his worthiness to combat Grendel through his words and actions. One line that shows this is when Beowulf says, 'Nothing afeard of what thyself didst make, Strange images of death.' Here, Beowulf is assuring Hrothgar that he is not afraid of the dangers that Hrothgar himself has faced. Another line that demonstrates Beowulf's persuasion is when he says, 'Thy praises in his kingdom's great defence, And pour'd them down before him.' By telling Hrothgar that his praises have been sung in defense of his kingdom, Beowulf is showing his loyalty and commitment to protecting Hrothgar's people.