sich reimen
to rhyme
Describes that two or more words sound the same or very similar at the end.
Die Wörter „Nacht“ und „Macht“ reimen sich.
The words 'Nacht' and 'Macht' rhyme.

to rhyme
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to rhyme
Describes that two or more words sound the same or very similar at the end.
Die Wörter „Nacht“ und „Macht“ reimen sich.
The words 'Nacht' and 'Macht' rhyme.

In its basic meaning, 'reimen' is reflexive ('sich reimen', to rhyme). To name the matching rhyming word, you use the preposition 'auf' with the accusative.
Das Wort „Haus“ reimt sich auf „Maus“.
The word 'Haus' rhymes with 'Maus'.
'Sich reimen' describes a property of words (they sound the same). The non-reflexive 'reimen' describes an active action by a person: writing poetry or creating rhymes.
Die Wörter „Sonne“ und „Wonne“ reimen sich.
The words 'Sonne' and 'Wonne' rhyme.
The expression 'sich (Dativ) etwas zusammenreimen' means that you draw a conclusion from clues. The prefix 'zusammen-' emphasizes the putting together of information here.
Aus seinen wenigen Worten konnte ich mir den Rest der Geschichte zusammenreimen.
From his few words, I was able to piece together the rest of the story.
When you cannot understand something at all, you use the fixed idiom 'sich keinen Reim auf etwas machen können' (to not be able to make sense of something). The person is in the dative, and the incomprehensible thing follows after 'auf' in the accusative.
Ich kann mir auf sein plötzliches Verschwinden absolut keinen Reim machen.
I absolutely can't make sense of his sudden disappearance.
to understand
'verstehen' and 'reimen' are connected here only in certain fixed expressions. 'verstehen' directly says that you grasp the meaning of something. With 'sich etwas zusammenreimen' (to piece something together), you try to find an explanation from a few clues. That is less certain than real understanding. The contrast is especially clear in 'sich keinen Reim auf etwas machen können' (to be unable to make sense of something): this means that you do not understand something at all or cannot explain it to yourself. Learners may confuse the words because 'Reim' here has nothing to do with poems, but is used figuratively.

Ich kann mir keinen Reim darauf machen, warum die Tür heute Morgen offen war.
I can't make sense of why the door was open this morning.
Nach der Erklärung verstehe ich endlich, warum der Termin verschoben wurde.
After the explanation, I finally understand why the appointment was postponed.