
abnehmen
to lose weight
To reduce one's own body weight; to lose weight.
Ich versuche, durch Sport und gesunde Ernährung etwas abzunehmen.
I'm trying to lose a little weight through exercise and healthy eating.
to lose weight / decrease / take off
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to lose weight
To reduce one's own body weight; to lose weight.
Ich versuche, durch Sport und gesunde Ernährung etwas abzunehmen.
I'm trying to lose a little weight through exercise and healthy eating.

to decrease
To become less; to decrease in amount, strength, or intensity.
Gegen Abend hat der Wind deutlich abgenommen.
Toward evening, the wind decreased noticeably.

to take off
To remove something from a surface or from the body.
Er nahm seine Brille ab, um sie zu putzen.
He took off his glasses to clean them.

to answer
To pick up the receiver of a telephone in order to take a call.
Das Telefon klingelt schon seit einer Minute, warum nimmt niemand ab?
The phone has been ringing for a minute already; why isn't anyone answering?

to take away
To take something away from someone, often in an official context.
Die Polizei hat dem Fahrer den Führerschein abgenommen.
The police took the driver's license away from the driver.

to believe
To believe something someone says; to consider a statement true.
Seine Ausrede war so seltsam, dass ich sie ihm nicht abnehme.
His excuse was so strange that I don't believe it.

to administer
To officially conduct and evaluate an exam or test.
Der Prüfer wird Ihnen morgen die mündliche Prüfung abnehmen.
The examiner will administer your oral exam tomorrow.

to take from someone
To take a task or burden away from someone in order to relieve them.
Soll ich dir die schweren Taschen abnehmen?
Should I take the heavy bags from you?
'Abnehmen' is a separable verb. The prefix 'ab-' stands at the end in a main clause; in a subordinate clause it remains attached to the verb, and in the infinitive with 'zu', 'zu' comes between 'ab' and 'nehmen'.
Er nimmt jeden Tag seine Mütze ab, wenn er nach Hause kommt.
He takes off his cap every day when he comes home.
Many meanings of 'abnehmen' use a structure with two objects: the person is in the dative, and the thing involved is in the accusative. So the pattern is: subject + nimmt + dative object (person) + accusative object (thing) + ab.
Der Polizist nahm dem Raser den Führerschein ab.
The police officer took the speeder's driver's license away.
When 'abnehmen' means to lose weight, it is often used without an object. The subject is always the person who is losing weight.
Sie hat in den letzten Monaten fünf Kilo abgenommen.
She has lost five kilos in the last few months.
In the meaning 'to become less', 'abnehmen' usually refers to natural phenomena or abstract things. Typical subjects are the wind, noise, strength, or interest.
Die Begeisterung für das Projekt hat stark abgenommen.
Enthusiasm for the project has decreased sharply.
When it is about removing something, the objects are often things that are worn on the body or that cover something. Typical examples are: 'den Hut abnehmen' (to take off one's hat), 'die Maske abnehmen' (to take off the mask), 'den Deckel abnehmen' (to take off the lid).
Bitte nehmen Sie vor dem Betreten des Tempels den Hut ab.
Please take off your hat before entering the temple.
When 'abnehmen' means 'to believe', the accusative object is often something abstract such as 'die Geschichte' (the story), 'die Ausrede' (the excuse), or an entire subordinate clause with 'dass' (that).
Ich nehme ihm seine Entschuldigung nicht ab.
I don't believe his apology.
In the meaning 'to relieve someone', 'abnehmen' is very often phrased as a polite question to offer someone help. Typical objects here are 'die Tasche' (the bag), 'der Koffer' (the suitcase), or 'die Arbeit' (the work).
Das sieht schwer aus, soll ich dir den Koffer abnehmen?
That looks heavy; should I take the suitcase from you?
The meaning 'to pick up the receiver' is specific to making phone calls. The verb is used without an object here. You often hear it as a request.
Kann bitte jemand abnehmen? Das Telefon klingelt ununterbrochen.
Can someone please answer? The phone is ringing nonstop.
to lose
When referring to a reduction in body weight, both verlieren and abnehmen are possible, but the sentence structure is different. Verlieren takes the weight as its object, whereas abnehmen describes the change undergone by the person. So you say that someone loses five kilos, but that they take five kilos off with abnehmen.

Mara hat in drei Monaten fünf Kilo abgenommen.
Mara lost five kilos in three months.
Mara hat in drei Monaten fünf Kilo verloren.
Mara lost five kilos in three months.