In German, der Mann and die Frau are the standard, everyday words for “man” and “woman,” while der Herr and die Dame are formal, polite terms roughly equivalent to “gentleman” and “lady.” The plural forms die Damen and die Herren have historically been used for formal address, announcements, and signs. 

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Wenn Sie unsicher sind, meine Damen und Herren, dann rufen Sie bitte lieber die Polizei.

If you are unsure, ladies and gentlemen, then it's better to please call the police.

Caption 31, Großstadtrevier: Von Monstern und Mördern

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All four of these nouns can be used in compound nouns, such as der Frauenfußball ("women's football"). Compound nouns related to human rights, healthcare, sports leagues, and demographics tend to include Frauen and Männer, whereas those with Damen and Herren would more likely relate to retail categories, sports gear, and public facilities.

Das ist eine Jacke, besser gesagt, ein Damenjackett.

This is a jacket, or better said, a ladies' jacket.

Caption 19, Eva zeigt uns: Kleidungsstücke

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Anfang des zwanzigsten Jahrhunderts waren Frauenrechte noch stark eingeschränkt.

At the beginning of the twentieth century, women's rights were still severely restricted.

Captions 5-6, Gleichberechtigung: Internationaler Frauentag am 8. März

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When it comes to addressing a group of people, there are quite a few standard gender-inclusive phrases that allow you to avoid using Meine Damen und Herren or gendered noun endings.

Hallo, liebe Leute!

Hello, dear people! 

Caption 1, Weihnachten in Deutschland: Schneeflöckchen, Weißröckchen

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Hallo zusammen. Heute sind wir bei der Firma Ekomo in Bruchsal. 

Hello, everyone. Today we are at the company Ekomo in Bruchsal. 

Caption 1, Neko-Induktionsheizung: Interview mit Mirja Löhr

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Liebe Gäste, und jetzt ein kleines Konzert von unseren guten Freunden:

Dear guests, and now a little concert from our good friends:

Captions 21-22, Nicos Weg: Theater und Konzerte

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Beispiele dafür sind: „Studierende“, „Lehrende“ oder „Mitarbeitende“.

Examples of this are: "students," "teachers," or "employees."

Captions 32-33, LGBTQ Gendern

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In formal letters or emails, Sehr geehrtes Team is widely accepted for addressing a group, or Guten Tag [full name] for an individual.

Further Learning

You can learn more about this topic, including how the German language deals with pronouns, in this video on Yabla German.