
das Dach
roof
The top covering of a building that protects it from weather such as rain and snow.
Nach dem Sturm musste das Dach repariert werden.
After the storm, the roof had to be repaired.
roof
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roof
The top covering of a building that protects it from weather such as rain and snow.
Nach dem Sturm musste das Dach repariert werden.
After the storm, the roof had to be repaired.

to have a roof over one's head
To have shelter or a home; not to be homeless.
Er war dankbar, nach der Flucht schnell wieder ein Dach über dem Kopf zu haben.
He was grateful to have a roof over his head again quickly after fleeing.

under one roof
To live or work together in the same building.
Die drei Generationen der Familie leben alle unter einem Dach.
The three generations of the family all live under one roof.

to get on someone's case
To sharply reprimand someone or confront them angrily.
Wenn du dein Zimmer nicht aufräumst, steigt dir deine Mutter aufs Dach.
If you don't tidy your room, your mother will get on your case.
'Dach' (roof) is a very productive base word in German. You find it in many compounds that refer to the upper part of a house, such as 'Dachgeschoss' (attic floor/top floor), 'Dachfenster' (roof window/skylight), 'Dachterrasse' (roof terrace), or 'Dachziegel' (roof tile).
Wir wohnen im Dachgeschoss und haben eine kleine Dachterrasse.
We live on the top floor and have a small roof terrace.
Pay attention to the case with prepositions. 'Auf dem Dach' (on the roof; dative) describes a position, while 'aufs Dach' (onto the roof; accusative) describes movement.
Der Schornsteinfeger arbeitet auf dem Dach.
The chimney sweep is working on the roof.
The expression 'ein Dach über dem Kopf haben' (to have a roof over one's head) means, figuratively, to have a home or safe shelter. It is often used to express a basic need.
Solange ich ein Dach über dem Kopf und genug zu essen habe, bin ich zufrieden.
As long as I have a roof over my head and enough to eat, I'm satisfied.
The phrase 'unter einem Dach' (under one roof) is often used to emphasize that several people or groups live or work together in the same house/building.
Die Firma vereint mehrere Abteilungen unter einem Dach.
The company brings several departments together under one roof.
In the colloquial expression 'jemandem aufs Dach steigen' (to get on someone's case), the person being criticized is always in the dative. It means to confront someone angrily.
Mein Chef ist mir heute wegen des Fehlers richtig aufs Dach gestiegen.
My boss really got on my case today because of the mistake.