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.

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.
hand
'die Hand' and 'der Arm' are both parts of the body and are directly connected. That is why learners can easily confuse them. 'der Arm' extends from the shoulder to the hand. 'die Hand' is only the part at the end of the arm with the fingers. When you grasp something, write, or touch someone, you usually use your hand. When it is about lifting, carrying, or pain between the shoulder and the hand, 'Arm' often fits. Memory tip: the hand is part of the arm.

Nach dem Training tut ihr rechter Arm weh.
After training, her right arm hurts.
Er hält die heiße Tasse vorsichtig in der Hand.
He carefully holds the hot cup in his hand.