
begegnen
to meet
To meet someone by chance. This verb is used with the dative.
Gestern bin ich in der Stadt meiner alten Schulfreundin begegnet.
Yesterday I met my old school friend in town.
to encounter / meet
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to meet
To meet someone by chance. This verb is used with the dative.
Gestern bin ich in der Stadt meiner alten Schulfreundin begegnet.
Yesterday I met my old school friend in town.

to confront / address
To face something (e.g., a challenge, a problem, a danger) or deal with it in a particular way.
Wir müssen der Klimakrise mit entschlossenen Maßnahmen begegnen.
We must address the climate crisis with decisive measures.

to treat / approach
To show a particular behavior toward someone or something; to treat someone in a particular way.
Er begegnet seinen Mitarbeitern immer mit großem Respekt.
He always treats his employees with great respect.
The verb 'begegnen' (to encounter/meet) always requires the dative. You encounter 'jemandem' (someone, dative) and not 'jemanden' (someone, accusative). This is an important rule and a common source of mistakes.
Auf dem Weg zur Arbeit bin ich meinem Chef begegnet.
On the way to work, I ran into my boss.
The perfect tense of 'begegnen' is always formed with the auxiliary verb 'sein' (to be), not with 'haben' (to have). So the correct form is 'ich bin begegnet' (I have encountered/met).
Bist du ihm danach noch einmal begegnet?
Did you meet him again after that?
'Begegnen' is an inseparable verb. The prefix 'be-' remains firmly attached to the verb stem in all conjugated forms and sentence positions. The past participle is 'begegnet' (without 'ge-').
Ich hoffe, dass ich ihr morgen auf der Konferenz begegne.
I hope that I meet her tomorrow at the conference.
In the figurative meaning, 'begegnen' is often used with abstract nouns in the dative, for example 'einer Gefahr begegnen' (to confront a danger), 'einem Problem begegnen' (to address a problem), or 'einer Herausforderung begegnen' (to face a challenge).
Das Unternehmen muss den neuen Herausforderungen des Marktes begegnen.
The company must address the new challenges of the market.
To express the manner of treatment, 'begegnen' is often combined with an adverb (e.g., 'freundlich' (kindly), 'offen' (openly)) or a prepositional phrase (e.g., 'mit Respekt' (with respect)).
Sie begegnet neuen Ideen immer sehr offen.
She always approaches new ideas very openly.
to put / to set
Both sich einer Herausforderung stellen and einer Herausforderung begegnen can express an active response. Sich stellen emphasizes consciously accepting the confrontation, while begegnen places more emphasis on the response or on how one deals with it. Use stellen for readiness and begegnen for the concrete response.

Sie begegnet der schwierigen Aufgabe mit großer Ruhe.
She responds to the difficult task with great calm.
Sie stellt sich der schwierigen Aufgabe und beginnt sofort.
She faces the difficult task and gets started immediately.