hochhalten
to hold up
To lift something up with the hands or arms and hold it there so that it is clearly visible.
Die Demonstranten hielten ihre Plakate hoch.
The demonstrators held up their signs.

to hold up
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to hold up
To lift something up with the hands or arms and hold it there so that it is clearly visible.
Die Demonstranten hielten ihre Plakate hoch.
The demonstrators held up their signs.

'Hochhalten' (to hold up) is a separable verb. In a main clause, the prefix 'hoch' comes at the end. In subordinate clauses or in the infinitive with 'zu', the verb stays together.
Die Siegerin hält den Pokal stolz hoch.
The winner proudly holds up the trophy.
The object reveals the meaning: if someone holds up a concrete object, the literal meaning is intended. With an abstract concept like 'Werte' (values) or 'Tradition' (tradition), the figurative meaning is intended. In a sports context, it usually refers to a ball.
Er hielt das Baby hoch, damit es alle sehen konnten.
He held up the baby so that everyone could see it.
In the figurative meaning, 'hochhalten' (to uphold) is often used with abstract nouns. Typical combinations are 'die Tradition hochhalten' (to uphold the tradition), 'die Ehre hochhalten' (to uphold honor), 'Werte hochhalten' (to uphold values), or 'das Andenken an jemanden hochhalten' (to honor someone's memory).
Auch in schwierigen Zeiten müssen wir die Ideale der Gerechtigkeit hochhalten.
Even in difficult times, we must uphold the ideals of justice.
to preserve
'wahren' and 'hochhalten' can both mean that you do not give up values, rules, or traditions. 'wahren' is more neutral and somewhat more formal. For example, you can 'Ruhe wahren' (keep calm), 'Abstand wahren' (keep your distance), 'Rechte wahren' (preserve rights), or 'den guten Ruf wahren' (preserve a good reputation). It emphasizes that something is protected and preserved. 'hochhalten' sounds more strongly like respect and a public stance. You uphold values, traditions, or memories because you consider them important. Learners may confuse the words because both are used with abstract things. As a guide: 'wahren' fits when something is meant to be preserved or protected; 'hochhalten' fits when you consciously honor something and show that it is important.

Der Verein hält die Tradition des gemeinsamen Sommerfests seit vielen Jahren hoch.
The club has upheld the tradition of the shared summer festival for many years.
Auch im Streit versucht Maria, ihre Ruhe zu wahren.
Even during an argument, Maria tries to keep calm.