
trauen
to trust
To place trust in someone; to believe that someone is honest and reliable.
Nach der schlechten Erfahrung traut sie niemandem mehr.
After the bad experience, she doesn't trust anyone anymore.
to trust / dare / marry
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to trust
To place trust in someone; to believe that someone is honest and reliable.
Nach der schlechten Erfahrung traut sie niemandem mehr.
After the bad experience, she doesn't trust anyone anymore.

to dare
To have the courage to do something that one sees as risky, difficult, or unpleasant.
Ich traue mich nicht, vor so vielen Leuten zu sprechen.
I don't dare speak in front of so many people.

to marry
As a priest or registrar, to perform a marriage ceremony.
Der Bürgermeister persönlich hat das Paar getraut.
The mayor personally married the couple.
You can recognize the meaning of 'trauen' from the grammar. 'Jemandem trauen' (to trust someone, with dative) means to trust. 'Sich trauen' (to dare, reflexive) means to have courage. 'Jemanden trauen' (to marry someone, with accusative) means to perform a marriage ceremony.
Ich traue meinem besten Freund vollkommen.
I trust my best friend completely.
The verb 'trauen' is closely related to the noun 'das Vertrauen' (trust, confidence) and 'die Trauung' (wedding ceremony). All of these words have to do with belief, bonds, and reliability.
Vertrauen ist die Basis jeder guten Beziehung.
Trust is the basis of every good relationship.
When 'trauen' means 'vertrauen' (to trust), the person you trust is always in the dative. A common mistake is using the accusative.
Kann man diesem Politiker wirklich trauen?
Can one really trust this politician?
In the meaning 'Mut haben' (to have courage), 'trauen' is always reflexive ('sich trauen'). It is usually followed by an infinitive construction with 'zu', which describes what someone dares to do.
Sie traut sich, ihre Meinung offen zu sagen.
She dares to state her opinion openly.
When an official person marries a couple, 'trauen' is used with an accusative object. The subject is the person conducting the ceremony (e.g., the priest), and the object is the couple.
Ein Kapitän darf auf hoher See Paare trauen.
A captain may marry couples on the high seas.
to set / put
Setzen auf someone and jemandem trauen both express trust. Setzen auf emphasizes a deliberate choice and the expectation that the person will succeed. Trauen places greater emphasis on personal trust that the person is honest and reliable.

Der Trainer traut der jungen Torhüterin, weil sie immer zuverlässig handelt.
The coach trusts the young goalkeeper because she always acts reliably.
Der Trainer setzt im wichtigen Finale auf die junge Torhüterin.
The coach is counting on the young goalkeeper in the important final.