I thought that the only way of expressing possession using the verb gehören is jdm gehören, but in a movie I heard:
"Ich gehöre zu der Gemeinsamkeit."
Are the two forms interchangeable?
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The key difference is
being property of someone: jdm. gehören
Das Buch gehört mir.
being part of something: zu jdm/etw. gehören
Ich gehöre zu der Gruppe.
For example, there's a song by "Die Ärzte" with the following text:
Ich bin dein Diener, du der Herr
ab heut' gehör' ich dir allein.
Bitte laß mich dein Sklave sein!
It's about "possession", here namely about being a slave.
In contrast, there's a song by "Marianne Rosenberg" with the following text:
Er gehört zu mir, wie mein Name an der Tür.
It's not about possession, but about complementing each other and each one being a part of the whole.
"Ich gehöre dir" and "Ich gehöre zu dir" are two differing things. And they are not interchangeably.
In your sentences, it's about being a part of something, so you go with zu jdm./etw. gehören.
Gehören has a few more meanings but I think they're unrelated to this question. You can look them up in any dictionary.