
verdrehen
to twist
To move something out of its normal shape or position by twisting; to sprain or wrench something.
Ich bin beim Sport unglücklich gefallen und habe mir das Knie verdreht.
I fell awkwardly while doing sports and twisted my knee.
to twist / distort
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to twist
To move something out of its normal shape or position by twisting; to sprain or wrench something.
Ich bin beim Sport unglücklich gefallen und habe mir das Knie verdreht.
I fell awkwardly while doing sports and twisted my knee.

to distort
To intentionally present the meaning of facts, statements, or the truth incorrectly or in a distorted way.
Der Anwalt warf dem Zeugen vor, die Tatsachen zu verdrehen.
The lawyer accused the witness of distorting the facts.

to roll one's eyes
To roll one's eyes upward as a sign of annoyance, impatience, or disbelief.
Jedes Mal, wenn seine Mutter ihn an die Hausaufgaben erinnerte, konnte er nur die Augen verdrehen.
Every time his mother reminded him about his homework, all he could do was roll his eyes.
'Verdrehen' (to twist / distort) is an inseparable verb. The prefix 'ver-' remains firmly attached to the stem 'drehen' (to turn) in all tenses and sentence constructions. It often indicates that something is being made wrong or brought into a bad state.
Er hat die Fakten in seiner Aussage komplett verdreht.
He completely distorted the facts in his statement.
When someone injures a body part, 'verdrehen' (to twist) is used reflexively. The person is in the dative, and the body part is in the accusative: 'sich (dative) etwas (accusative) verdrehen' (to twist something).
Die Sportlerin hat sich im Spiel den Knöchel verdreht.
The athlete twisted her ankle during the game.
When it is about lying or manipulation, 'verdrehen' (to distort) is used with abstract nouns such as 'die Wahrheit' (the truth), 'die Tatsachen' (the facts), or 'die Worte' (the words). A fixed expression is 'jemandem die Worte im Mund verdrehen' (to twist someone's words).
Hör auf, mir die Worte im Mund zu verdrehen! Das habe ich so nicht gesagt.
Stop twisting my words! That's not what I said.
The expression 'die Augen verdrehen' (to roll one's eyes) is a fixed unit. It always expresses annoyance, irritation, or impatience, and the object is always 'die Augen' (the eyes).
Als er die gleiche Frage zum dritten Mal stellte, verdrehte sie genervt die Augen.
When he asked the same question for the third time, she rolled her eyes in annoyance.
to roll
Mit den Augen rollen and die Augen verdrehen both refer to the same gesture expressing annoyance, impatience, or disbelief. The key difference is the fixed expression: rollen is used with „mit den Augen“, whereas verdrehen is used with „die Augen“.

Als er dieselbe Frage noch einmal hörte, verdrehte er genervt die Augen.
When he heard the same question again, he rolled his eyes in annoyance.
Als er dieselbe Frage noch einmal hörte, rollte er genervt mit den Augen.
When he heard the same question again, he rolled his eyes in annoyance.