
die Tatsache
fact
A state of affairs or circumstance that is demonstrably true and recognized as really existing; a fact.
Es ist eine unbestreitbare Tatsache, dass der Klimawandel existiert.
It is an undeniable fact that climate change exists.
fact
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fact
A state of affairs or circumstance that is demonstrably true and recognized as really existing; a fact.
Es ist eine unbestreitbare Tatsache, dass der Klimawandel existiert.
It is an undeniable fact that climate change exists.

the fact is that ...
A fixed expression used to emphasize an indisputable point or bring a discussion back to the facts.
Tatsache ist, dass wir ohne weitere Investitionen das Projekt nicht beenden können.
The fact is that without further investment, we cannot finish the project.

to present someone with a fait accompli
To confront someone with a situation that has already happened and can no longer be changed, without informing or involving them beforehand.
Sie hat einfach den Flug gebucht und mich damit vor vollendete Tatsachen gestellt.
She simply booked the flight and thereby presented me with a fait accompli.
The word is made up of 'Tat' (deed/action) and 'Sache' (thing/matter). A 'Tat' is something that was done, an action. So a 'Tatsache' (fact) is literally an 'action-thing', a state of affairs that really happened and is therefore provable.
Es ist eine Tatsache, dass er den Vertrag unterschrieben hat.
It is a fact that he signed the contract.
'Tatsache' (fact) is very often used to introduce a subordinate clause with 'dass' (that). The construction 'die Tatsache, dass ...' (the fact that ...) functions as a noun phrase in the sentence.
Die Tatsache, dass er zu spät kam, hat alle geärgert.
The fact that he came late annoyed everyone.
The phrase 'Tatsache ist, dass ...' (the fact is that ...) appears at the beginning of a sentence to make an indisputable point. It introduces a subordinate clause with 'dass' (that), in which the conjugated verb comes at the end.
Tatsache ist, dass die Frist morgen abläuft und wir noch nicht fertig sind.
The fact is that the deadline is tomorrow and we are not finished yet.
The idiom 'jemanden vor vollendete Tatsachen stellen' (to present someone with a fait accompli) is a fixed unit. The person who is surprised is always in the accusative.
Er hat das Auto einfach gekauft und seine Frau damit vor vollendete Tatsachen gestellt.
He simply bought the car and thereby presented his wife with a fait accompli.
truth
Wahrheit concerns whether a statement corresponds to reality. Tatsache, on the other hand, is a single demonstrably true state of affairs. Wahrheit is appropriate for an honest or correct statement, while Tatsache is used for an established circumstance.

Der Polizeibericht bestätigt die Tatsache, dass die Ampel rot war.
The police report confirms the fact that the traffic light was red.
Der Zeuge sagt über den Unfall die Wahrheit.
The witness is telling the truth about the accident.