The ancient Greeks worshiped their gods for the same reason that any spiritual-religious people engage in worship: they believed that their gods were real, that those gods desired worship and reverence, and that those gods would reward those who worshiped them. While the Greek notion of "god" and "gods" changed significantly over the centuries, the fundamental reason for worshipping them did not.
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Yes,some do!
burnt offerings and temples of worship
their kids when they ate they would burn a portion of their food in a fire
Greek gods were imagined by the Greeks, so they are related by that.
The Romans built temples because they kind of copied the Greek civilizations. After all, they had to worship gods. They had the same gods as the Greeks, but in different names. For example, Zeus in Greece was Jupiter in Roman.