In German, there are several different ways to talk about avoiding something or someone. 

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The verb that is used most often is probably vermeiden. You can use it to describe avoiding a situation or something you have to do. 

So vermeidest du am leichtesten eine peinliche Situation,

That's the easiest way for you to avoid an embarrassing situation

Caption 62, Deutsch mit Eylin: Tischsitten

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Der Schreiadler vermeidet die Konfrontation.

The lesser spotted eagle avoids confrontation.

Caption 16, Expeditionen ins Tierreich: Die Feldberger Seen

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Habe das einmal sieben, habe ich lang vermieden.

For a long time, I avoided the seven times table. 

Caption 83, Nena: Das 1x1 mit den Hits von NENA

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The verb meiden is similar, but generally used to describe staying away from something or someone, rather than an active effort to avoid doing something. 

Selbst Murmeltiere meiden diese Gegend.

Even marmots avoid this area.

Caption 17, Die letzten Paradiese - Schätze der Natur: Südtirol 

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The verb ausweichen is used when it comes to physically avoiding something in the sense of dodging it. 

Wildwasserkajaks sind extrem wendig, um den vielen Hindernissen im Fluss rasch ausweichen zu können.

Whitewater kayaks are extremely maneuverable so that they can quickly dodge the many obstacles in the river.

Captions 41-42, Die letzten Paradiese: Die Schönheit der Alpen 2

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When it comes to avoiding a person, there is also the phrase (jemandem) aus dem Weg gehen. 

Ich geh dir aus dem Weg, will dich ignorieren.

I avoid you, I want to ignore you.

Caption 7, LOTTE: Schau mich nicht so an

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Further Learning
Use each of these verbs in a sentence, or look up more examples with vermeiden on Yabla German.

In a recent lesson, we took a look at the German phrases zu Fuß, Kopf bis Fuß, ohne Hand und Fuß, Fuß fassen and der Fuß (the US and UK standard measurement "foot"). Today, let's check out some other German phrases using der Fuß.

Doch ich steh mittlerweile mehr als mit einem Fuß im Knast

But I've got more than one foot in jail now

Caption 39, Cro: Bad Chick

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The phrase mit einem Fuß im... is similar to the English phrase: "with one foot in the grave", and generally means "to be near" to whatever is referred to. German also uses mit einem Fuß im Grab and, with the same meaning, mit einem Fuß im Jenseits ("...in the afterlife"). The caption above means he was close to being in prison before, but is now actually in prison!

Doch dann stößt er am Fuß des Conturines-Massivs in 2.008 Metern auf eine riesige Höhle.

But then he comes across, at the foot of the Conturines massif at 2,008 meters, a huge cave.

Captions 5-6, Die letzten Paradiese: Schätze der Natur

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A "massif" is the main mass of a mountain, and indeed the expression "at the foot of the mountain" —that is to say, "the base of the mountain"—is the same as the German am Fuß des Berges.

Wenn wir da einen Fuß reinkriegen, dann ziehe ich ganz runter und schaffe mir einen Harem an.

When we get a foot in the door  then I'll move down there completely and get myself a harem.

Captions 8-9, Mama arbeitet wieder: Alle haben sich lieb

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The German idiom einen Fuß reinkriegen (literally "to get a foot in") means the same as the English idiom "to get one's foot in the door," a figurative way of saying "to gain entry" or "to get an opportunity."

Da haben Sie mich gerade auf dem falschen Fuß erwischt.

You have just caught me on the wrong foot.

Caption 34, Tanz in den Mai: "Ladies Get Wild"

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The German idiom auf dem falschen Fuß erwischt means "to be caught unprepared" or "to be surprised." This is somewhat different from the English expression "to get off on the wrong foot," which means "to have a bad start."

Ich will ja niemandem auf die Füße treten.

I don't want to step on anyone's feet.

Caption 10, Coronavirus: Nikolaus mit Mundschutz

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The German and English idioms are the same here: "to step on someone's feet" is a figurative way of saying "to upset someone."

Further Learning
It's always interesting how some languages have idioms that are the same as your native language. But it's especially interesting to learn the expressions that are different and sound very odd if you translate them directly! Take a look at the videos above on Yabla German to get a better feel for the contexts in which they are used.