personal pronouns - Possessives ("his", "her") versus definite article ("the")

"He led her by the hand."

"I hit him in the jaw."

"She closed her eyes."

In the first two examples one doesn't say "her hand" and in the second one doesn't say "his jaw". But in the third one says "her eyes" and not "the eyes".

Is there a rule governing the choice between "the" and the possessive forms?