How do you know if you have a Morgan silver dollar?

A Morgan silver dollar is a large dollar coin, on the front there should be a depiction of Lady Liberty's face wearing a small crown saying "LIBERTY" on it the reverse features an eagle with olive branches and arrows and a wreath at the bottom. They were dated 1878 to 1904 and also made in 1921. The only other coin that could be easily confused with a Morgan dollar is a Peace Dollar of which some were also minted in 1921, they have the same size, but the liberty on a Peace dollar looks like there are rays coming out of her head and the reverse of a Peace dollar has an eagle perched on a rock engraved PEACE.