to fit together
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to go together
To harmonize; to go well together in terms of qualities, appearance, or character.
Ich finde, die neue Couch und der Teppich passen farblich nicht gut zusammen.
I think the new couch and the rug don't go together well in terms of color.
'Zusammenpassen' (to fit together) is a separable verb. The prefix 'zusammen' (together) goes at the end of the main clause; in a subordinate clause it stays connected to the verb, and in the infinitive with 'zu', 'zu' stands between the two parts.
Diese beiden Farben passen gut zusammen.
These two colors go well together.
The word consists of the adverb 'zusammen' (together) and the verb 'passen' (to fit). The meaning is very literal: things or people 'passen' (fit) 'zusammen' (together).
Die Teile des Schranks passen nicht zusammen.
The parts of the cabinet don't fit together.
When it is about harmony, the verb is often combined with adverbs such as 'gut' (well), 'perfekt' (perfectly), 'überhaupt nicht' (not at all), or 'wunderbar' (wonderfully). You can also describe the aspect more precisely, e.g. 'charakterlich' (in terms of character) or 'optisch' (visually) zusammenpassen.
Als Paar haben sie charakterlich nie wirklich zusammengepasst.
As a couple, they never really went together in terms of character.
You can recognize this meaning by the fact that it is about physical objects that are supposed to connect. Typical subjects are puzzle pieces, building blocks, a key and lock, or machine parts.
Der Deckel und der Topf passen nicht zusammen.
The lid and the pot don't fit together.
to fit / suit / pass
'passen' and 'zusammenpassen' both have to do with something being right or harmonious. 'Passen' is often used when a single thing is right for a person, an appointment, or a situation: 'Die Jacke passt' (the jacket fits), 'der Termin passt' (the appointment works). 'Zusammenpassen' is used when two or more things go well together or can be connected with each other. So it emphasizes the relationship between the parts. Learners may confuse the words because both occur with clothing, colors, people, or objects. As a simple guide: something 'passt zu' something; two things 'passen zusammen'.
Der rote Schal und die schwarze Jacke passen gut zusammen.
The red scarf and the black jacket go well together.
Die neuen Schuhe passen mir gut, aber sie sind etwas teuer.
The new shoes fit me well, but they are a bit expensive.