A number of German verbs have legen as a root. Let's go alphabetically and explore some of the most common words. 

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The verbs auflegen and einlegen each have a number of different translations. The verb auflegen describes putting something on top of something else and, by extension, can mean "to hang up the phone" or "to play music as a DJ." It is also used to refer to publishing an edition. The verb einlegen literally means "to put something into something," which can be physical in the case of fermenting or pickling vegetables (eingelegtes Gemüse) or immaterial in the case of raising an objection (Einspruch einlegen) or taking a break (eine Pause einlegen). 

Max? -Henri, ich muss jetzt leider auflegen.

Max? -Henri, I have to hang up now, unfortunately.

Caption 28, Die Pfefferkörner: Endspurt

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Erschöpft legen Franz Obermeier, seine Söhne und Helfer eine Pause ein.

Exhausted, Franz Obermeier, his sons and helpers take a break.

Caption 8, Die letzten Paradiese Schätze der Natur: Südtirol

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The verb festlegen is more straightforward, as it is always related to determining, defining, or ascertaining something. 

Figuren und Reitstil sind seit Jahrhunderten genau festgelegt.

The figures and riding style have been precisely defined for centuries.

Caption 46, Die Alpen von oben - S1 E2: Von Graz ins Ausseerland

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And sich hinlegen simply means "to lie down." 

Es legte sich hin und schlief sofort ein.

She laid herself down and immediately fell asleep.

Caption 43, Märchen - Sagenhaft: Goldlöckchen und die drei Bären

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You'll hear the verb loslegen quite often at the beginning of Yabla videos: 

Ja, ja, das geht dann auch schneller. -Na, dann lass uns loslegen!

Yes, yes, then it will also go faster. -Well, then let's get started!

Caption 44, Abenteuer Nordsee: Unter Riesenhaien und Tintenfischen

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The verb offenlegen means "to reveal."

Das Null-zu-null beim leidenschaftlich kämpfenden Hamburger SV legte das Problem des Rekordmeisters offen.

The zero to zero outcome against a Hamburg squad, [ho fought passionately, revealed the master record champion's main problem.

Captions 19-20, Fußball pur Paderborn: im Rausch

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The first non-separable verb of our list is überlegen, "to consider."  

Schön... Lass mich mal überlegen.

Nice... Let me think about it.

Caption 28, Deutsch mit Eylin: Anruf bei einer neuen Bekannten

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The verb verlegen means "to misplace" or "to lose," but it is also an adjective that means "embarrassed." 

„Ach so, hm“, meinte Frederick verlegen. „Dann können wir ja weitergehen.“

"Ah, so, hm," said Frederick sheepishly. "Then, indeed, we can keep walking."

Caption 34, Piggeldy und Frederick: Das Lachen

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The verb zurücklegen means "to put back," but also "to cover" in the context below:

Elftausend Kilometer haben Sie mit dem Fahrrad zurückgelegt.

You have traveled eleven thousand kilometers [nearly seven thousand miles] with the bicycle.

Caption 8, Mountainbiken: Auf dem Anden-Trail

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Further Learning
You'll find many videos with these verbs used in context on Yabla German. You can also do a search for many other verbs with the root legen, such as ablegen, anlegen, beilegen, freilegen, and more. 

This week, let's review the vocabulary in German for political and geographical subdivisions. We will start from the largest subdivisions and proceed to the smallest.

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Dann natürlich auch, um 'nen fremden Kontinent kennenzulernen,

Then of course also in order to get to know an unfamiliar continent,

weil man aufm Fahrrad eigentlich so nah dran ist wie sonst nicht, wenn man reist.

because on the bicycle you actually are so much closer to it than when you otherwise travel.

Captions 14-15, Mountainbiken - Auf dem Anden-Trail

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Welches Land ist ein Nachbarland von Deutschland?

Which country is a neighboring country of Germany?

Caption 27, Bundesrepublik Deutschland - Einbürgerungstest - Part 14

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Die Region zwischen Amrum und Sylt wurde wegen der Meeressäuger unter Schutz gestellt.

The region between Amrum and Sylt was placed under protection because of the marine mammals.

Caption 2, Abenteuer Nordsee - Unter Riesenhaien und Tintenfischen

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You probably already know the word die Stadt ("the city") and related words like die Hauptstadt or die Großstadt. The word der Staat is not to be confused with die Stadt. Although the United States is die Vereinigten Staaten in German, the word used for a federal state is generally das Bundesland. Der Staat is more often used when referring to something being done or provided by the federal or state government. 

Es ist sein erster Besuch in Berlin als Präsident der Vereinigten Staaten von Amerika.

It is his first visit to Berlin as the president of the United States of America.

Caption 4, Angela Merkel - Gemeinsame Pressekonferenz mit Barack Obama

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Der Staat muss die Gesetze einhalten.

The state has to abide by the laws.

Caption 4, Bundesrepublik Deutschland - Einbürgerungstest - Part 7

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In Deutschland gibt es in jedem Bundesland sogenannte Landeshauptstädte.

In Germany, there are so-called state capitals in each federal state.

Caption 15, Bundesländer und ihre Spezialitäten - Baden-Württemberg

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When speaking about a district of a city, or a "quarter," the German word is der Bezirk or der Stadtteil or das Viertel. The word der Kiez is used in certain cities on an informal basis to denote a particular part of a district that may even be just a few square blocks. In these places, it is much more commonly used than die Nachbarschaft. 

Hallo, ich stehe hier am Eingang des Viktoriaparks im Berliner Stadtteil Kreuzberg.

Hello, I am standing here at the entrance of Viktoriapark in the Berlin district of Kreuzberg.

Caption 1, Berlin - Eva im Viktoriapark

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Gitarrist Jürgen Ehle wohnt seit fünfundzwanzig Jahren

Guitarist Jürgen Ehle has lived for twenty-five years

in dem Kiez und schwelgt in Erinnerungen.

in the neighborhood, and luxuriates in memories.

Captions 3-4, Pankow - Rolling Stones des Ostens

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In German, die Kleinstadt specifies a town rather than a city. To talk about rural life, there is das Dorf ("the village") and also die Gemeinde, which can be used for a rural community as well as an urban one. 

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Further Learning
Practice these words and their correct articles by describing where you live. Begin with the smallest area unit and progress until you are at continent level! Yabla German can provide more examples using these words if you get stuck on the declensions.