
nahe
near / close
Describes a short spatial distance to something or someone.
Wir wohnen ganz nahe am Bahnhof.
We live very close to the train station.
near / close
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near / close
Describes a short spatial distance to something or someone.
Wir wohnen ganz nahe am Bahnhof.
We live very close to the train station.

close
Describes a close personal, emotional, or family relationship.
Sie ist eine nahe Verwandte von mir.
She is a close relative of mine.

near
Describes a short distance in time; something that is coming soon.
Der Abschied war nahe und alle waren traurig.
The farewell was near, and everyone was sad.

to suggest
To strongly recommend something to someone or give them something to consider.
Die Spuren am Tatort legen den Verdacht nahe, dass der Täter Handschuhe trug.
The traces at the crime scene suggest the suspicion that the perpetrator wore gloves.

to offend someone
To offend or hurt someone through a remark or action, or to disregard their privacy.
Ich will Ihnen nicht zu nahe treten, aber Ihr Vorschlag ist nicht durchdacht.
I don't want to offend you, but your proposal is not well thought out.
The adjective 'nahe' (near/close) belongs to the word family of 'die Nähe' (proximity/closeness). Both express a short distance, whether spatial, temporal, or emotional.
Ich suche eine Wohnung in der Nähe des Parks.
I'm looking for an apartment near the park.
The word 'nahe' (near/close) is often used with the dative to express the relationship to something or someone. A preposition is not always necessary.
Das Geschäft liegt dem Bahnhof nahe.
The shop is located near the train station.
In the context of personal relationships, 'nahe' (close) is often combined with 'Verwandte' (relatives) or 'Freunde' (friends). The phrase 'sich nahestehen' means to have a very close relationship.
Nur die nahen Angehörigen waren zur Beerdigung eingeladen.
Only the close relatives were invited to the funeral.
The phrase 'jemandem etwas nahelegen' (to suggest/recommend something to someone) is a fixed construction. The person is in the dative, and the thing being recommended is in the accusative.
Ich möchte dir dringend nahelegen, noch einmal darüber nachzudenken.
I would strongly suggest that you think about it again.
The idiom 'jemandem zu nahe treten' (to offend someone / get too personal with someone) is a fixed construction. The person whom you might potentially hurt is always in the dative.
Ohne Ihnen zu nahe treten zu wollen, aber diese Krawatte passt nicht zu Ihrem Hemd.
Without meaning to offend you, but this tie does not match your shirt.
narrow / close / tight
Nahe and eng can both describe a strong personal relationship. Nahe particularly emphasizes the feeling of emotional closeness, while eng tends to highlight the intensity and lasting nature of the relationship. Use nahe for a personal feeling, and eng often for the nature of the relationship.

Nach unserem offenen Gespräch fühle ich mich meiner Schwester wieder nahe.
After our open conversation, I feel close to my sister again.
Auch nach vielen Jahren habe ich eine enge Beziehung zu meiner Schwester.
Even after many years, I have a close relationship with my sister.