It is not surprising that the king of the Greek gods would be identified with the majestic eagle. After all, the eagle soars the skies and sees all, much like Zeus sits on his throne in lofty Mount Olympus and surveys his kingdom.
The thunderbolt is Zeus's weapon.
The throne is a symbol of royalty. Zeus was respected as a very powerful god, and so the throne is used to symbolize him.
Zeus appears in the form of a bull in a few stories from mythology. Of these tales, one of the most famous is of the god and his encounter with a woman named