
entgegentreten
to oppose
To actively resist or confront someone or something. This can refer to a person, an opinion, a danger, or a problem.
Wir müssen diesen falschen Gerüchten entschieden entgegentreten.
We must firmly oppose these false rumors.
to oppose / approach
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to oppose
To actively resist or confront someone or something. This can refer to a person, an opinion, a danger, or a problem.
Wir müssen diesen falschen Gerüchten entschieden entgegentreten.
We must firmly oppose these false rumors.

to approach
To go toward someone in order to meet or greet them. This meaning is more literal and less common.
Als er aus dem Zug stieg, trat ihm sein alter Freund lächelnd entgegen.
When he got off the train, his old friend approached him with a smile.
'Entgegentreten' (to oppose/approach) is a separable verb. The prefix 'entgegen-' is separated from the verb in a main clause and placed at the end of the sentence. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Sie tritt der Ungerechtigkeit mutig entgegen.
She bravely stands up to injustice.
This verb always requires the dative. You say 'jemandem' or 'etwas' entgegentreten, not 'jemanden' or 'etwas'.
Der Politiker trat der Kritik der Journalisten entgegen.
The politician opposed the journalists' criticism.
In the meaning 'sich widersetzen' (to resist/oppose), the verb is often combined with abstract nouns. Typical examples are: 'einer Gefahr entgegentreten' (to confront a danger), 'einem Problem entgegentreten' (to tackle a problem), 'der Kritik entgegentreten' (to counter criticism), or 'Vorurteilen entgegentreten' (to oppose prejudices).
Die Bürgerinitiative will den Bauplänen der Stadt entgegentreten.
The citizens' initiative wants to oppose the city's building plans.
This literal meaning is less common and is found more in written language. You can recognize it by the fact that one person physically moves toward another, often in a positive or neutral context.
Als sie ankam, trat ihr die ganze Familie freudig entgegen.
When she arrived, the whole family came toward her joyfully.
to contradict
Widersprechen means explicitly disagreeing with a person or opinion. Entgegentreten refers to a more active approach against a position and can go beyond a single statement. Use widersprechen for a specific opposing opinion; entgegentreten is better for ongoing or practical resistance.

Jana tritt dem Vorurteil mit einer öffentlichen Informationskampagne entgegen.
Jana confronts the prejudice with a public information campaign.
Jana widerspricht ihrem Kollegen, als er das Vorurteil wiederholt.
Jana contradicts her colleague when he repeats the prejudice.