beweisen
to prove
To demonstrate the correctness or truth of a statement or situation with facts, arguments, or evidence.
Der Angeklagte konnte seine Unschuld vor Gericht beweisen.
The defendant was able to prove his innocence in court.

to prove
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to prove
To demonstrate the correctness or truth of a statement or situation with facts, arguments, or evidence.
Der Angeklagte konnte seine Unschuld vor Gericht beweisen.
The defendant was able to prove his innocence in court.

The verb 'beweisen' (to prove) is inseparable. The prefix 'be-' remains firmly attached to the verb stem 'weisen' in all sentence forms and tenses.
Sie beweist immer wieder ihren Mut.
She proves her courage again and again.
'Beweisen' (to prove) is very often used with a person in the dative and a thing in the accusative. The structure is: jemand (subject) beweist jemandem (dative) etwas (accusative).
Der Anwalt konnte dem Richter die Unschuld seines Mandanten beweisen.
The lawyer was able to prove his client's innocence to the judge.
In the context of facts and truth, 'beweisen' (to prove) is often combined with legal or scientific nouns. Typical examples are: 'die Unschuld beweisen' (to prove innocence), 'das Gegenteil beweisen' (to prove the opposite), or 'eine Hypothese beweisen' (to prove a hypothesis).
Mit diesem Experiment wollen die Forscher ihre Hypothese beweisen.
With this experiment, the researchers want to prove their hypothesis.
When the point is to demonstrate a quality, 'beweisen' (to prove) is often used with abstract nouns such as Mut (courage), Stärke (strength), Talent (talent), or Geduld (patience).
In der schwierigen Situation hat sie echte Stärke bewiesen.
In the difficult situation, she proved real strength.
The reflexive form 'sich beweisen' (to prove oneself) means to demonstrate one's own abilities. The reflexive pronoun 'sich' is adapted to the person (ich muss mich beweisen, du musst dich beweisen).
Im neuen Job musste er sich von Anfang an beweisen.
In the new job, he had to prove himself from the very beginning.
to show
'zeigen' and 'beweisen' can both express that something becomes clear. 'zeigen' is broader and weaker: a behavior, a result, or a sign can point to something or make something visible. 'beweisen' is stronger. It means that you make it clear with facts, arguments, or an action that something is really true. Learners often confuse the words because in both cases you are supporting a statement. If it is only an indication, 'zeigen' fits. If there is clear evidence, 'beweisen' fits.

Morgen müssen wir beweisen, dass die Maschine wieder sicher läuft.
Tomorrow we have to prove that the machine is running safely again.
Die vielen Fragen zeigen, dass das Thema noch nicht klar ist.
The many questions show that the topic is still not clear.