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.
'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 encounter / meet
'begegnen' and 'entgegentreten' can both describe dealing with a problem, a danger, or an opinion. 'Einer Schwierigkeit begegnen' (to address a difficulty) means: you react to it or deal with it. This can be meant in a calm, factual, or general way. 'Einer Sache entgegentreten' (to oppose something) is stronger. It means that you actively stand against something or fight it, for example a danger, a false statement, or a problem. So 'begegnen' fits when dealing with something, while 'entgegentreten' is for clear resistance.
Die Schule tritt Gewalt auf dem Schulhof klar entgegen.
The school takes a clear stand against violence in the schoolyard.
Wir begegnen der neuen Aufgabe mit Geduld und guter Planung.
We approach the new task with patience and good planning.