
der Arm
arm
The part of the human body that extends from the shoulder to the hand.
Ich habe mir beim Sport den rechten Arm gebrochen.
I broke my right arm while playing sports.
arm
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arm
The part of the human body that extends from the shoulder to the hand.
Ich habe mir beim Sport den rechten Arm gebrochen.
I broke my right arm while playing sports.

arm
A part of an object that resembles an arm in shape or function, e.g. on an armchair, a crane, or a river.
Der alte Sessel hat sehr bequeme Arme zum Ablegen der Ellbogen.
The old armchair has very comfortable arms for resting your elbows.

to pull someone's leg
To make fun of someone by telling them something untrue; to tease or fool someone.
Glaub ihm nicht alles, er nimmt dich nur auf den Arm.
Don't believe everything he says; he's just pulling your leg.

to lend a hand
To help or support someone, often financially or with a difficult task.
Als ich arbeitslos war, haben mir meine Eltern finanziell unter die Arme gegriffen.
When I was unemployed, my parents lent me a financial hand.

arm / branch
A branch or division of a larger organization.
Die Stiftung ist der wohltätige Arm des Unternehmens.
The foundation is the charitable arm of the company.
Do not confuse the noun 'der Arm' (arm, body part) with the adjective 'arm' (poor, having little money). You can recognize the noun by the article and the capitalization.
Der arme Junge hat sich den Arm verletzt.
The poor boy injured his arm.
The idiom 'jemanden auf den Arm nehmen' (to pull someone's leg) means to make fun of someone or tease them. The person being teased is in the accusative.
Glaub ihm nicht, er nimmt dich nur auf den Arm.
Don't believe him; he's just pulling your leg.
The idiom 'jemandem unter die Arme greifen' (to lend someone a hand) means to support someone, often financially or with a difficult task. The person being helped is in the dative.
Als sie krank war, hat ihre Nachbarin ihr oft unter die Arme gegriffen.
When she was sick, her neighbor often lent her a hand.
The context shows whether 'Arm' (arm) is meant literally or figuratively. In connection with the body, it is literal (m01). As part of an object (e.g. 'Sesselarm' (arm of an armchair), 'Flussarm' (branch of a river)) or an organization, the meaning is metaphorical (m02, m05).
Der Kran hat einen langen Arm.
The crane has a long arm.
As a body part, 'Arm' (arm) is often used with verbs such as 'heben' (to raise), 'ausstrecken' (to stretch out), or 'verschränken' (to fold/cross). The expression 'jemanden in den Arm nehmen' means 'to hug someone.'
Zum Abschied nahm er seine Mutter fest in den Arm.
He gave his mother a tight hug when saying goodbye.
department
Der Arm and die Abteilung can both refer to an organizational part of a larger institution. Abteilung is the neutral, concrete term for a clearly defined division, while Arm emphasizes a branch or affiliated side of the organization. Abteilung is usually suitable for internal divisions; Arm can also be used for organizational branches.

Der soziale Arm der Organisation betreut Familien in der Stadt.
The organization’s social arm supports families in the city.
Die Abteilung für soziale Arbeit betreut Familien in der Stadt.
The social work department supports families in the city.