
der Haken
hook
A curved object made of metal or plastic that is used to hang up or fasten something.
Häng deine Jacke bitte an den Haken an der Wand.
Please hang your jacket on the hook on the wall.
hook / catch
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hook
A curved object made of metal or plastic that is used to hang up or fasten something.
Häng deine Jacke bitte an den Haken an der Wand.
Please hang your jacket on the hook on the wall.

catch
An unexpected difficulty, disadvantage, or hidden problem in something that otherwise seems good.
Das Angebot klingt super, aber es muss doch irgendwo einen Haken geben.
The offer sounds great, but there must be a catch somewhere.

check mark
A mark (✓) that you make to mark something on a list as done or to indicate a correct answer.
Bitte mach hinter jeden Punkt, den du erledigt hast, einen Haken.
Please put a check mark after each item you have completed.

hook
A short sideways punch in boxing.
Der Boxer traf seinen Gegner mit einem schnellen linken Haken.
The boxer hit his opponent with a quick left hook.
The figurative meaning is very often used in the question 'Wo ist der Haken?' (What's the catch?). You use it to ask about the hidden disadvantage in an offer that sounds too good to be true.
Ein kostenloses Smartphone? Da muss es doch einen Haken geben.
A free smartphone? There must be a catch.
When referring to the physical object, it is almost always combined with the verb 'hängen' (to hang) and the preposition 'an' (on/at).
Kannst du meinen Mantel bitte an den Haken hängen?
Can you please hang my coat on the hook?
In the meaning of 'Häkchen' (check mark), the verb 'machen' (to make) or 'setzen' (to place/put) is often used. You make or put a check mark after a task on a list.
Ich habe alle Punkte erledigt und überall einen Haken gemacht.
I completed all the items and put a check mark everywhere.
The meaning 'Boxschlag' (boxing punch) is very specific. It is used exclusively in the context of sports, especially boxing or martial arts.
Er beendete den Kampf mit einem gezielten Haken.
He ended the fight with a well-aimed hook.
to chop / hack
Der Haken refers to the problematic or hidden disadvantage in something that is otherwise good. Hacken, by contrast, describes a mechanical device jerking or briefly jamming. Use der Haken for the problem itself and hacken for the uneven functioning of a device.

Der Haken an dem günstigen Angebot ist die lange Vertragslaufzeit.
The catch with the inexpensive offer is the long contract term.
Das Getriebe beginnt beim Anfahren zu hacken.
The gearbox starts to jerk when pulling away.