
hängend
hanging
Describes something that hangs down from above or has a downward-tilted position.
Die Weide am Ufer hat lange, hängende Zweige.
The willow by the bank has long, hanging branches.
hanging / pending
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hanging
Describes something that hangs down from above or has a downward-tilted position.
Die Weide am Ufer hat lange, hängende Zweige.
The willow by the bank has long, hanging branches.

pending
In legal and administrative language: not yet completed or decided; currently being processed.
Während des hängenden Verfahrens darf der Angeklagte das Land nicht verlassen.
During the pending proceedings, the defendant may not leave the country.
The word 'hängend' (hanging) is the present participle of the verb 'hängen' (to hang). This form describes an ongoing state or an ongoing action and is used like an adjective.
Die hängenden Pflanzen auf dem Balkon müssen gegossen werden.
The hanging plants on the balcony need to be watered.
You can recognize the meaning from the context. If 'hängend' (hanging) refers to physical objects such as branches or shoulders, it means 'hanging down'. In legal or administrative texts in connection with 'Verfahren' (proceedings) or 'Klage' (lawsuit), it means 'pending' or 'being processed'.
Mit hängenden Schultern ging er nach Hause.
He went home with drooping shoulders.
In its literal meaning, 'hängend' (hanging) is often used to describe body parts or parts of plants. Typical combinations are 'hängende Schultern' (drooping shoulders), 'hängende Mundwinkel' (downturned corners of the mouth), or 'hängende Geranien' (hanging geraniums).
Der alte Baum hat tief hängende Äste.
The old tree has low-hanging branches.
The meaning 'in Bearbeitung' (being processed) belongs to legal and administrative language. This usage is not used in normal everyday speech.
Die Klage ist seit zwei Jahren bei diesem Gericht hängend.
The lawsuit has been pending at this court for two years.
open
An open administrative matter simply has not yet been completed or decided. In legal and administrative language, “hängend” additionally means that a procedure is still ongoing or being processed. In everyday language, “offen” is appropriate; in a specialized administrative text, “hängend” may be suitable.

Im Schreiben der Behörde wird das Verfahren als hängend bezeichnet.
The authority’s letter describes the procedure as pending.
Die Entscheidung über den Antrag ist noch offen.
The decision on the application is still open.