Cheetahs use these tear lines to block the sun out of their eyes. Just like football player when they put the black make up on to get the glaring of the sun out of harms way. So cheetahs use these tear lines to walk around for new territory or hunting with running. That's why the cheetahs have tear lines
One way you can tell a cheetah from other spotted cats is by the dark lines that run from its eyes to its mouth. These lines are called "tear lines". These dark areas may help to protect the cheetah's eyes from the glare of the sun. Have you seen a football player have black lines under there eyes when they play? They protect their eyes just like the cheetah does.
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they have tear marks to symbolize their outcast to society. they are unique animals and don't fit in with the rest of the African wilderness.
Cheetahs have it so when a enemy or a lion try to attack they'll get confused and probably think it's an honey badger. That way they'll be safe.
They may be serving as a shield for the eyes against the sun's glare, a helpful feature as the cheetah hunts mainly during the day; another purpose could be to define facial expressions.