die Treue
loyalty / fidelity
The quality of being steadfast, loyal, and reliable toward a person, cause, belief, or promise.
Er hat seine Treue zu diesem Verein über viele Jahre bewiesen.
He has proven his loyalty to this club over many years.

loyalty / fidelity
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loyalty / fidelity
The quality of being steadfast, loyal, and reliable toward a person, cause, belief, or promise.
Er hat seine Treue zu diesem Verein über viele Jahre bewiesen.
He has proven his loyalty to this club over many years.

'Die Treue' (loyalty / fidelity) is the noun corresponding to the adjective 'treu' (loyal / faithful). If you know what 'treu' means, you can easily derive the meaning of 'die Treue'.
Ein treuer Freund ist ein Geschenk.
A loyal friend is a gift.
'Treue' is often combined with certain verbs. The most important fixed combinations are 'jemandem die Treue halten' (to remain loyal to someone), 'jemandem die Treue schwören' (to swear loyalty/fidelity to someone), and 'die Treue brechen' (to break one's loyalty/fidelity).
Die Fans halten ihrem Verein auch in schlechten Zeiten die Treue.
The fans remain loyal to their club even in difficult times.
Loyalty to a person or thing is expressed with the preposition 'zu' and the dative. In the expression 'jemandem die Treue halten' (to remain loyal to someone), the person is also in the dative.
Ihre Treue zu ihren Prinzipien war bewundernswert.
Her loyalty to her principles was admirable.
'Nach Treu und Glauben' (in good faith) is a fixed term from legal language. It describes the expectation that contracting parties behave honestly and fairly. It is used almost only in formal or legal contexts.
Man muss im Geschäftsleben nach Treu und Glauben handeln.
In business, one must act in good faith.
agreement / correspondence
'die Treue' and 'die Übereinstimmung' can both express that something matches an original, a model, or the facts. 'Treue' is often used in this sense when a representation stays close to the original, for example in a translation or film adaptation. 'Übereinstimmung' is more general: two things, statements, or pieces of data fit together or are the same. 'Treue' sounds more strongly connected to an original, while 'Übereinstimmung' is more about a comparison between two sides.

Bei der Übersetzung achtet Sofia auf die Treue zum Originaltext.
When translating, Sofia pays attention to faithfulness to the original text.
Die Polizei prüft die Übereinstimmung der Aussagen.
The police are checking whether the statements match.