I have noticed that English tends to use possessive adjectives like "his" in situations for which German would leave them out. For example I would say "er wäscht sich die Hände" rather than "er wäscht seine Hände." The latter would be the most literal translation of "he washes his hands" in English, but it seems like it would be wrong in German.
Are there any definite rules for when to leave out the possessive adjectives in German? In these cases, is it always necessary to specify "sich" (or mir etc. as the case may be) plus the definite article, or can I leave that and use only the article when it is obvious from context who the things in question belong to?