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.

This week we're going to continue to go through cases used with German prepositions. If you are an advanced German speaker, this will be nothing new for you, but will hopefully be helpful for beginners as a learning tool and for intermediate German speakers as a refresher. Nouns, pronouns, and adjectives that are modified by prepositions take either the accusative, dative, or genitive case, but to make things slightly confusing, some prepositions require either the accusative or dative case, depending upon the context. In Part II today, let's examine the prepositions that always require the dative case for nouns, pronouns, and adjectives. 

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Let's start out by taking a look at the dative case for nouns as follows for the definite article "the," with the nominative case followed by the dative case: 

der => dem
die => der
das => dem

And for the indefinite article: 

ein (masculine) => einem
eine => einer
ein (neuter) => einem

And for the singular and plural personal pronouns "I," "you," "he," "she," , "it," "we," and "they":

ich => mir
du => dir
Sie (formal "you") => Ihnen
er => ihm
sie => ihr
es => ihm
ihr => euch
wir => uns
sie => ihnen
Sie (formal "you" plural) => Ihnen

Remember too that if there is no definite or indefinite article, the adjective must still take the case appropriate for its gender with the preposition.

The common German prepositions that require the dative case of nouns and pronouns are aus, außer, bei, gegenüber, mit, nach, seit, von, and zu. Here are some examples from Yabla German. The article in the feminine noun die Mode becomes der in the dative case.

Die gute alte Kaffeemaschine

The good old coffee machine

ist dabei etwas aus der Mode geraten.

has to some extent gone out of style in the process.

Caption 12, Eva zeigt uns - wie man Kaffee kocht

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Here, the nominative pronoun ich becomes mir in the dative case:

In diesem Haus wohnen außer mir

In this house live, other than me,

noch mehrere Familien in Mietwohnungen.

several other families in rental apartments.

Captions 5-6, Zu Besuch bei Jenny - Am Hauseingang

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Here, the indefinite feminine article eine (for die Flasche) becomes einer in the dative case, and the neuter ein (for das Glas) becomes the dative einem:

Ob es sich bei einer Flasche oder einem Glas um eine Mehrweg- oder Pfandflasche handelt...

With a bottle or a jar, whether it happens to be returnable or a bottle with a deposit...

Caption 48, Eva erklärt - Mülltrennung

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The dative preposition gegenüber is a bit unusual, in that when it is used on its own, it falls after the item it modifies:

Dem Clubhaus gegenüber liegt ein feiner Sandstrand.

Across from the clubhouse lies a fine sandy beach.

Caption 31, Golf - in Wien

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You can see this above in the correct word order dem Clubhaus gegenüber (not gegenüber dem Clubhaus!). If you wanted to place gegenüber before das Clubhaus, however, you must add the dative preposition von to the mix. So it would also be acceptable to formulate the sentence above as Gegenüber von dem Clubhaus liegt ein feiner Sandstrand. This would be translated exactly the same into English.

Here, the nominative pronoun ihr becomes euch in the dative case:

Jasmin und ich werden heute mit euch üben.

Jasmin and I will practice with you today.

Caption 2, Diane erklärt - Fragewörter

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And here, the masculine indefinite article ein (for der Monat) becomes the dative einem:

Erst nach einem Monat bleibt das Küken fast den ganzen Tag alleine.

Only after a month, the chick stays alone almost all day.

Caption 30, Alpenseen - Kühle Schönheiten

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The feminine definite article die (for die Römerzeit) becomes the dative der:

... seit der Römerzeit ein befestigter Alpenübergang.

... since Roman times a fortified Alpine crossing.

Caption 23, Die letzten Paradiese - Die Schönheit der Alpen 2

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With the preposition von, the nominative pronoun er becomes the dative pronoun ihm:

Es ist genau das, was seine Anhänger von ihm hören wollen.

It is exactly what his supporters want to hear from him.

Caption 25, Tagesschau - Amtseinführung von Donald Trump 

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And finishing up our A to Z of dative pronouns, the nominative pronoun du becomes dir in the dative:

Sorry, das läuft auf meinem alten Laptop nicht. Da müssen wir zu dir.

Sorry, this doesn't run on my old laptop. We'll have to go to your place.

Caption 35, Die Pfefferkörner - Gerüchteküche

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Further Learning
To recap, the common German prepositions that require the dative case of nouns and pronouns are aus, außer, bei, gegenüber, mit, nach, seit, von, and zu. Go to Yabla German to look for more examples of prepositions whose nouns, pronouns, and adjectives take only the dative case. Also review Part I in this series about prepositions that require the accusative case.