
tragen
to wear
To have clothing, jewelry, or glasses on one's body.
Heute trage ich meinen neuen Pullover.
Today I'm wearing my new sweater.
to wear / carry
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to wear
To have clothing, jewelry, or glasses on one's body.
Heute trage ich meinen neuen Pullover.
Today I'm wearing my new sweater.

to carry
To move something from one place to another with one's hands or on one's body.
Kannst du mir helfen, den schweren Koffer zu tragen?
Can you help me carry the heavy suitcase?

to support
To hold or support the weight of something, often in an architectural or structural sense.
Diese alten Balken tragen das gesamte Dach.
These old beams support the entire roof.

to bear
To take on the responsibility, consequences, or costs for something.
Der Verursacher des Unfalls muss den Schaden tragen.
The person who caused the accident must bear the cost of the damage.

to bear
To produce fruit or blossoms, in reference to plants.
Unser Apfelbaum trägt dieses Jahr zum ersten Mal.
Our apple tree is bearing fruit for the first time this year.

to bear
To have a name, title, or designation.
Das neue Forschungsinstitut trägt den Namen Marie Curies.
The new research institute bears Marie Curie's name.

to be carrying
To be pregnant or have offspring inside one's body, used for animals and in elevated language for humans.
Die Stute trägt ein Fohlen.
The mare is carrying a foal.

to bear fruit
An idiom meaning that an effort or plan leads to positive results and is successful.
Nach monatelanger Arbeit beginnt das Projekt endlich, Früchte zu tragen.
After months of work, the project is finally beginning to bear fruit.
In almost all of its meanings, 'tragen' is a transitive verb that requires an accusative object. The question is: Whom or what does someone/something carry, wear, support, or bear?
Sie trägt einen eleganten Hut.
She is wearing an elegant hat.
The perfect tense of 'tragen' is always formed with the auxiliary verb 'haben' (to have). This also applies when you carry something from one place to another, meaning when movement takes place.
Ich habe die schwere Kiste allein in den Keller getragen.
I carried the heavy box down to the basement by myself.
When the object of the verb is a piece of clothing, glasses, jewelry, or an accessory, 'tragen' means 'am Körper haben' (to wear / to have on one's body).
Er trägt selten einen Anzug.
He rarely wears a suit.
When it is about moving an object with the hands or body, a direction or destination is often mentioned in the sentence. This helps you recognize the meaning 'transportieren' (to transport/carry).
Die Mutter trägt ihr schlafendes Kind ins Bett.
The mother carries her sleeping child to bed.
In the meaning 'stützen' (to support), the subject is often a structural element such as a column, a beam, or a foundation. The object is then the weight or another part of the structure.
Diese Säulen tragen das gesamte Gewölbe der Kirche.
These columns support the entire vault of the church.
In the abstract meaning 'übernehmen' (to take on), 'tragen' is combined with specific nouns. Typical ones are: 'die Kosten tragen' (to bear the costs), 'die Verantwortung tragen' (to bear the responsibility), 'die Konsequenzen tragen' (to bear the consequences), or 'das Risiko tragen' (to bear the risk).
Als Projektleiter trägt er die volle Verantwortung.
As project manager, he bears full responsibility.
When it is about having a name or title, 'tragen' is used directly with the name or title as the object. This use is rather formal.
Die Brücke trägt den Namen eines berühmten Architekten.
The bridge bears the name of a famous architect.
The expression 'Früchte tragen' (to bear fruit) is based on the literal meaning used with plants. Idiomatically, it means that an effort has paid off and is leading to positive results.
Seine harte Arbeit hat endlich Früchte getragen und er wurde befördert.
His hard work finally bore fruit, and he was promoted.
to be called / to mean
Heißen and tragen can express the name something has. Heißen connects the name directly with the person or thing and sounds neutral. Tragen uses the name as an object and usually sounds more formal.

Das neue Kulturzentrum trägt den Namen Sonnenhof.
The new cultural center bears the name Sonnenhof.
Das neue Kulturzentrum heißt Sonnenhof.
The new cultural center is called Sonnenhof.