to defy / withstand
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to defy
To stubbornly, and often defiantly, resist an instruction, a person, or a situation. It is often used for children's behavior.
Das kleine Kind trotzte und wollte seine Jacke nicht anziehen.
The little child was defiant and did not want to put on his jacket.
The verb 'trotzen' (to defy / withstand) belongs to the word family of 'der Trotz' (defiance, the attitude of resistance) and the adjective 'trotzig' (defiant). When a child 'trotzt' (is defiant), it shows 'Trotz' (defiance) or is 'trotzig' (defiant).
Aus reinem Trotz wollte er nicht mit uns sprechen.
Out of pure defiance, he did not want to speak with us.
In the meaning of 'standhalten' (to withstand), 'trotzen' requires an object in the dative. This dative object is the force or condition being resisted.
Das kleine Boot trotzte den hohen Wellen.
The small boat withstood the high waves.
You can recognize the meaning from the subject and object. If it is about the behavior of people (often children) against an instruction, the first meaning is intended. If an object or person resists an external force (weather, danger), the second meaning is intended.
Der Junge trotzte seiner Mutter und aß das Gemüse nicht.
The boy defied his mother and did not eat the vegetables.
to endure / withstand
'aushalten' and 'trotzen' both describe not giving up under difficult conditions. 'aushalten' emphasizes enduring: you suffer from heat, pain, noise, or pressure, but you get through it. 'trotzen' sounds more active and stronger. It means to withstand a danger, a force, or bad conditions and not let yourself be defeated. It is often used with the dative, for example 'dem Sturm trotzen' (to defy the storm). Learners may confuse the words because both express 'not giving in'. As a simple guide: people or things 'halten etwas aus' (endure / withstand something); they are more likely to 'trotzen' a strong external force or danger.
Trotz des Regens trotzen wir dem schlechten Wetter und feiern im Garten.
Despite the rain, we defy the bad weather and celebrate in the garden.
Bei der Wanderung musste Mara die starke Hitze lange aushalten.
During the hike, Mara had to endure the intense heat for a long time.