getreu
faithful
Loyal and reliably committed to someone or something; faithful. The adjective is often used with a dative object.
Sie ist ihren Idealen immer getreu geblieben.
She has always remained faithful to her ideals.

faithful / true to
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faithful
Loyal and reliably committed to someone or something; faithful. The adjective is often used with a dative object.
Sie ist ihren Idealen immer getreu geblieben.
She has always remained faithful to her ideals.

'Getreu' (faithful / true to) is a more formal and often stronger variant of 'treu' (faithful). Both words belong to the word family around 'die Treue' (loyalty).
Er war ein treuer Freund in schweren Zeiten.
He was a loyal friend in difficult times.
When 'getreu' (faithful) expresses loyalty, the noun to which someone is faithful is in the dative. A typical construction is 'jemandem/etwas getreu bleiben' (to remain faithful to someone/something).
Der alte Diener blieb seinem Herrn bis zum Ende getreu.
The old servant remained faithful to his master until the end.
In the meaning of 'exakt entsprechend' (exactly corresponding), 'getreu' (true to) is often combined with nouns that describe an image or reproduction. Typical examples are 'eine getreue Kopie' (an exact copy) or 'eine getreue Darstellung' (a faithful depiction).
Das Museum stellt eine getreue Nachbildung des alten Stadttores aus.
The museum is exhibiting a faithful reproduction of the old city gate.
The expression 'getreu dem Motto' (true to the motto) introduces a sentence and explains the motivation for an action. The noun 'Motto' is always in the dative here.
Getreu dem Motto „Weniger ist mehr“ hat sie ihre Wohnung sehr minimalistisch eingerichtet.
True to the motto 'Less is more,' she furnished her apartment in a very minimalist way.
corresponding / according
'entsprechend' and 'getreu' can both mean that something fits a rule, model, or idea. 'entsprechend' is more general: you use it when something is done according to a rule or fits a situation. 'getreu' more strongly emphasizes that someone or something follows a model, an original, or a motto exactly. The words can be confused because both express a kind of correspondence. As a practical rule: for rules, plans, and suitable measures, 'entsprechend' is often more natural; for a motto, a model, or a very exact reproduction, 'getreu' fits better.

Getreu dem Motto „Weniger ist mehr“ hat Lisa das Zimmer sehr einfach eingerichtet.
True to the motto 'Less is more,' Lisa furnished the room very simply.
Entsprechend den Regeln müssen alle Besucher ihren Ausweis zeigen.
According to the rules, all visitors must show their ID.