
angehören
to be a member
To be a member of a group, organization, party, or family.
Sie gehört seit vielen Jahren dem örtlichen Schachclub an.
She has belonged to the local chess club for many years.
to belong to
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to be a member
To be a member of a group, organization, party, or family.
Sie gehört seit vielen Jahren dem örtlichen Schachclub an.
She has belonged to the local chess club for many years.

to belong to
To count as part of a particular category, genus, species, or era.
Diese Ruinen gehören der römischen Zeit an.
These ruins belong to the Roman period.
'Angehören' (to belong to) is a separable verb. The prefix 'an-' comes at the end in a main clause. In a subordinate clause or when used with a modal verb, the verb stays together.
Er gehört einer politischen Partei an.
He belongs to a political party.
The verb 'angehören' (to belong to) is always used with the dative. The group or category that someone or something belongs to is in the dative.
Dieses Kunstwerk gehört der Moderne an.
This work of art belongs to the modern era.
To express membership, the verb is often combined with social, political, or family groups. Typical phrases are: einer Partei angehören (to belong to a party), einem Verein angehören (to belong to a club/association), einer Familie angehören (to belong to a family).
Seit wann gehören Sie dem Vorstand an?
How long have you been a member of the board?
In this meaning, you can recognize the verb by the fact that it refers to abstract classifications. The object is then usually an era, a genus, a species, or a style.
Der Wal gehört der Gattung der Säugetiere an.
The whale belongs to the class of mammals.
to belong
Gehören zu and angehören can both express belonging to a group or category. Gehören normally requires zu in this meaning. Angehören is used without zu and connects directly with a group or category in the dative.

Lea gehört seit zwei Jahren diesem Verein an.
Lea has been a member of this club for two years.
Lea gehört seit zwei Jahren zu diesem Verein.
Lea has belonged to this club for two years.