Just like verbs, a large group of German adjectives carry a fixed preposition that is structurally bound to them and does not change; it cannot be chosen by logic or direct translation, but must be memorized together with the adjective as a single unit. This pattern is called Adjektive mit Präpositionen, and it appears most often in constructions of the type sein + adjective + preposition, where the adjective describes an emotional state or attitude toward a specific person or thing named afterward through the preposition.
For example, stolz auf (proud of) requires auf with the accusative, zufrieden mit (satisfied with) requires mit with the dative, and verliebt in (in love with) requires in with the accusative. There is no phonetic or semantic rule explaining why the language settled on one preposition rather than another for a given adjective; the assignment is as arbitrary as prepositional choices often are, where near-synonymous expressions can take different prepositions without a strict underlying logic.
In practice, these adjectives most often follow the verb sein, with the preposition placed directly after the adjective and the noun or pronoun following in the case the preposition requires: Ich bin stolz auf dich. When what follows the preposition is an entire clause rather than a noun, the same da-/wo- compounds used with verbs come into play: Ich bin stolz darauf, dass ich es geschafft habe (I am proud that I managed it), rather than placing a full clause directly after the preposition.
Certain semantic groupings help with memorization: auf and über often pair with emotions such as pride, anger, sadness, and joy; mit and von tend to mark relationships of dependence and satisfaction; an and für relate to interest and capability. These groupings are memory aids, not strict rules.
The most common mistake among learners is carrying over a preposition from their native language or from English, producing errors like stolz von instead of stolz auf, or forgetting to adjust the noun's case to match what the preposition demands, using accusative where dative is required or vice versa. The only reliable solution is to memorize each adjective together with its preposition and case as one inseparable unit, exactly as one memorizes vocabulary.