festigen
to strengthen
To strengthen or consolidate something abstract, such as a relationship, knowledge, or a position.
Durch regelmäßiges Üben festigte sie ihre Sprachkenntnisse.
Through regular practice, she strengthened her language skills.

to strengthen / consolidate
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to strengthen
To strengthen or consolidate something abstract, such as a relationship, knowledge, or a position.
Durch regelmäßiges Üben festigte sie ihre Sprachkenntnisse.
Through regular practice, she strengthened her language skills.

The verb 'festigen' (to strengthen/consolidate) is derived from the adjective 'fest' (firm), which means 'stable' or 'solid.' So 'festigen' literally means 'to make firm.'
Mit diesen Übungen können Sie Ihre Rückenmuskulatur festigen.
With these exercises, you can strengthen your back muscles.
In its non-reflexive form, 'festigen' (to strengthen/consolidate) is a transitive verb. It always needs an accusative object, meaning something that is being strengthened or consolidated.
Die Firma will ihre Position auf dem Markt festigen.
The company wants to consolidate its position in the market.
In a figurative sense, 'festigen' (to strengthen/consolidate) is often used with abstract concepts. Typical combinations are: 'eine Beziehung festigen' (to strengthen a relationship), 'eine Freundschaft festigen' (to strengthen a friendship), 'Wissen festigen' (to consolidate knowledge), or 'die eigene Macht festigen' (to consolidate one's own power).
Regelmäßige Wiederholung hilft, das Gelernte zu festigen.
Regular repetition helps consolidate what has been learned.
In its literal, physical meaning, the verb is often used in construction or geology. For example, you can say 'ein Fundament festigen' (to reinforce a foundation), 'den Boden festigen' (to stabilize the ground), or 'eine lockere Schraube festigen' (to tighten a loose screw).
Die Wurzeln der Bäume festigen den Hang.
The roots of the trees stabilize the slope.
When something becomes more stable on its own, the reflexive form 'sich festigen' (to become stronger/more stable) is used. The subject of the sentence is then the thing that is becoming firmer or more secure.
Seine Position im Unternehmen hat sich gefestigt.
His position in the company has become stronger.
to strengthen
'stärken' and 'festigen' can both mean that something becomes more secure, more stable, or more resilient. 'stärken' is broader and emphasizes greater strength or influence, for example with health, self-confidence, or a group. 'festigen' emphasizes stability and permanence more. It fits especially well with knowledge, relationships, rules, positions, or even something that becomes physically firmer. If something is meant to become stronger, 'stärken' is often natural. If something is meant to stand securely or remain stable in the long term, 'festigen' is more precise.

Mit vielen Übungen festigt Lisa ihr Wissen vor der Prüfung.
With lots of exercises, Lisa consolidates her knowledge before the exam.
Das gemeinsame Projekt stärkt das Vertrauen im Team.
The joint project strengthens trust within the team.