
verdient
deserved
Justified or appropriate because of achievement, effort, or behavior; well-deserved.
Nach der anstrengenden Woche hast du dir eine Pause redlich verdient.
After the exhausting week, you have truly deserved a break.
deserved
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deserved
Justified or appropriate because of achievement, effort, or behavior; well-deserved.
Nach der anstrengenden Woche hast du dir eine Pause redlich verdient.
After the exhausting week, you have truly deserved a break.

distinguished
Having earned recognition through many years of valuable work or special achievements; meritorious.
Professor Müller ist ein verdienter Forscher auf dem Gebiet der Zellbiologie.
Professor Müller is a distinguished researcher in the field of cell biology.
'Verdient' (deserved) is the past participle of the verb 'verdienen' (to earn / deserve). The meaning of the adjective comes directly from this: something that you have 'verdient' (deserved) through achievement or effort is 'verdient' (deserved).
Er hat hart für die Beförderung gearbeitet und sie sich wirklich verdient.
He worked hard for the promotion and really deserved it.
This adjective is often combined with positive results that are a reward for effort. Common phrases are 'ein verdienter Sieg' (a deserved victory), 'eine verdiente Pause' (a well-deserved break), or 'ein verdienter Urlaub' (a well-deserved vacation).
Nach dem Sieg feierte die Mannschaft ihren verdienten Erfolg.
After the victory, the team celebrated its well-deserved success.
When the adjective describes a person ('ein verdienter Mitarbeiter' — a distinguished employee), it is a formal and respectful way to honor that person's many years of valuable work. It is often used in official speeches or texts.
Die Universität ehrte die verdiente Professorin für ihr Lebenswerk.
The university honored the distinguished professor for her life's work.
fair / just
Gerecht evaluates a decision based on whether it is fair and impartial. Verdient describes a reward or consequence as appropriate because the person concerned earned it through their performance or behavior. Thus, for the same award, the process can be gerecht (fair) and the result verdient (deserved).

Die Auszeichnung für Mia war verdient, weil sie die beste Leistung gezeigt hatte.
The award for Mia was deserved because she had given the best performance.
Die Auszeichnung für Mia war gerecht, weil die Jury alle Leistungen nach denselben Regeln bewertete.
The award for Mia was fair because the jury evaluated everyone’s performance according to the same rules.