In the sentence
Du bist einer Maus ähnlich.
Why is ähnlich at the end of the sentence?
Ähnlich is placed there, because one of its uses is to compare:
In this use, ähnlich is said to be nachgestellt (put after, as some prepostions are). Moreover it is not qualifying, it's compairing the objects.
We have to see ähnlich as part of the verb. The verb is not sein but ähnlich sein. This is strongly supported by the fact that it rules its own case. Sein alone does not call for Dative at all. Adjectives however do not rule a case. In a different universe it might just be written as one word - ähnlichsein. It is similar to Fahrrad fahren or zurückgehen. There is no logical reason why one is written as 2 words and the other as one. Or even better... zumachen and zu sein
For all verbs there is a different level of adhesion between defining adverbials. For ähnlich it is not very strong and yet just as Fahrrad or the prefix ein, ähnlich is the "rest" of the predicate and thus at the end.
Just as with all verbs, I can add qualifiers ...and also particles.
And I can make comparisons with regular prefixes... although this is somewhat colloquial
Officially, this is wrong but it does not trigger a grammar alert as "den Tür" would do.