ziehen
to pull
To move something toward oneself or along behind oneself by applying force.
Das Kind zieht sein Spielzeugauto an einer Schnur hinter sich her.
The child pulls his toy car behind him on a string.

to pull / move
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to pull
To move something toward oneself or along behind oneself by applying force.
Das Kind zieht sein Spielzeugauto an einer Schnur hinter sich her.
The child pulls his toy car behind him on a string.

When 'ziehen' describes movement from one place to another (e.g. moving house, birds migrating), the perfect tense is formed with 'sein'. In most other meanings (e.g. pulling something, drawing a card), 'haben' is used.
Meine Nachbarn sind letzten Monat nach Berlin gezogen.
My neighbors moved to Berlin last month.
When you pull on a part of something, you use the preposition 'an' with the dative. Typical examples are pulling on a rope, a handle, or a door.
Du musst kräftig an dem Seil ziehen, um das Tor zu öffnen.
You have to pull hard on the rope to open the gate.
When talking about moving house, the destination is given with prepositions such as 'in' (+ accusative), 'nach' (for cities/countries without an article), or 'aufs' (for 'auf das Land'—to the countryside).
Sie möchte nächstes Jahr in eine größere Wohnung ziehen.
She wants to move into a larger apartment next year.
In the meaning 'etwas zufällig auswählen' (to select something randomly), 'ziehen' is often combined with objects such as 'eine Karte' (a card), 'ein Los' (a raffle ticket/lot), or 'eine Nummer' (a number).
Jeder Teilnehmer darf eine Nummer aus dem Hut ziehen.
Each participant may draw a number from the hat.
When a drink such as tea develops its aroma, 'ziehen' is used without an object. The drink itself is the subject of the sentence.
Der Tee muss fünf Minuten ziehen, bevor du ihn trinkst.
The tea needs to steep for five minutes before you drink it.
When drawing something on a surface, 'ziehen' is often used with objects such as 'eine Linie' (a line), 'einen Strich' (a stroke/line), 'einen Kreis' (a circle), or 'eine Grenze' (a boundary).
Er zog mit einem Bleistift eine gerade Linie.
He drew a straight line with a pencil.
The reflexive form 'sich ziehen' or 'sich hinziehen' means that something takes a very long time. It is often used for processes, negotiations, or construction work.
Die Besprechung zog sich bis in den späten Abend.
The meeting dragged on until late in the evening.
The expression 'einen Schluss ziehen' means to draw a logical conclusion. You can also use other abstract nouns, e.g. 'eine Konsequenz ziehen' (to draw a consequence) or 'eine Lehre ziehen' (to learn a lesson).
Aus diesem Fehler müssen wir eine Lehre für die Zukunft ziehen.
We have to learn a lesson from this mistake for the future.
The expression 'in Betracht ziehen' is a fixed combination and means 'überlegen' (to think about) or 'erwägen' (to consider). The noun 'Betracht' is used almost only in this expression.
Ich werde Ihr Angebot ernsthaft in Betracht ziehen.
I will seriously consider your offer.
to take
'nehmen' and 'ziehen' can both mean that you get or take something out of a set. 'nehmen' is more general: you grab something or choose something. 'ziehen' is used especially when the choice is random, for example with cards, lots, or numbers. The words can be confused because in both cases someone ends up holding something. If you choose deliberately, 'nehmen' usually fits. If chance decides, 'ziehen' sounds more natural.

Vor dem Spiel zieht jedes Kind eine Karte aus dem Stapel.
Before the game, each child draws a card from the deck.
Beim Frühstück nehme ich heute das Brot mit Käse.
At breakfast today, I'll have the bread with cheese.