
sich lehnen
to lean
To place one's body at an angle against something in order to find support and prop oneself up.
Er lehnte sich erschöpft gegen die Wand.
Exhausted, he leaned against the wall.
to lean
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to lean
To place one's body at an angle against something in order to find support and prop oneself up.
Er lehnte sich erschöpft gegen die Wand.
Exhausted, he leaned against the wall.

to lean
To place an object at an angle against something so that it is supported by it.
Kannst du die Leiter bitte an den Baum lehnen?
Can you please lean the ladder against the tree?

to go out on a limb
An idiom meaning to make too bold a claim, take too great a risk, or overstep one's authority.
Mit der Vorhersage, dass die Aktie um 50 % steigen wird, lehnst du dich sehr weit aus dem Fenster.
By predicting that the stock will rise by 50%, you're really going out on a limb.
Pay attention to the difference: 'sich lehnen' (to lean oneself; reflexive) means that a person supports their own body against something. 'Etwas lehnen' (to lean something; transitive) means that you place an object against something.
Sie lehnte sich müde an meine Schulter.
She leaned tiredly on my shoulder.
The verb 'lehnen' (to lean) is almost always used with a preposition that indicates the supporting surface. The most common are 'an' or 'gegen', followed by the accusative.
Lehn dich nicht gegen die frisch gestrichene Wand!
Don't lean against the freshly painted wall!
The idiom 'sich zu weit aus dem Fenster lehnen' (to lean too far out of the window) is a fixed unit. It is used metaphorically and means that someone says or does something too risky.
Mit dieser gewagten Prognose lehnst du dich wirklich weit aus dem Fenster.
With this bold forecast, you're really going out on a limb.
to support / lean
Here, lehnen describes an object's slanted position against a surface that supports it. Stützen, on the other hand, means actively holding an object in place or protecting it from falling over with an additional structure.

Die Leiter lehnt schräg an der Hauswand.
The ladder is leaning at an angle against the wall of the house.
Eine feste Strebe stützt die Leiter, damit sie nicht umfällt.
A sturdy brace supports the ladder so that it does not fall over.