congruent / identical
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identical
In a figurative sense, the complete agreement of opinions, interests, goals, or statements.
Unsere Vorstellungen für die Zukunft des Projekts sind nahezu deckungsgleich.
Our ideas for the future of the project are nearly identical.
The word is made up of 'Deckung' (coverage/overlap) and 'gleich' (same/equal). Here, 'Deckung' means 'coverage' or 'overlap.' Literally, it describes something that is 'the same' when overlapped, so it fits perfectly.
Die beiden Puzzleteile sind deckungsgleich und passen genau ineinander.
The two puzzle pieces are congruent and fit exactly into each other.
'Deckungsgleich' (congruent/identical) is very often used with the verb 'sein' (to be) to establish agreement between two or more things. The typical sentence pattern is: 'X und Y sind deckungsgleich' (X and Y are congruent/identical).
Ihre Interessen und meine Interessen sind vollkommen deckungsgleich.
Her interests and my interests are completely identical.
You can easily recognize the meaning from the context. If people are talking about geometry (figures, triangles, shapes), the literal meaning is intended. If it is about abstract things (opinions, plans, interests), the figurative meaning is intended.
In der Geometrie lernt man, wann zwei Dreiecke deckungsgleich sind.
In geometry, you learn when two triangles are congruent.
In the figurative meaning, 'deckungsgleich' (identical) is often combined with abstract nouns. Common combinations are: identical opinions, interests, goals, or ideas.
Die beiden Parteien haben nur wenige deckungsgleiche Ziele.
The two parties have only a few identical goals.
immediate / same
'gleich' and 'deckungsgleich' both describe that things match or correspond. 'gleich' is the normal, general word: two things can look the same, cost the same amount, or have the same meaning. 'deckungsgleich' is more precise and stronger. It means that something matches completely, for example shapes in geometry or goals and opinions in a figurative sense. Learners may confuse the words because both express agreement or correspondence. In everyday language, 'gleich' usually sounds more natural. 'deckungsgleich' is more suitable when you want to emphasize an exact or complete match.
Nach dem Gespräch waren unsere Ziele für das Projekt deckungsgleich.
After the conversation, our goals for the project were identical.
Die beiden Jacken sehen gleich aus, aber eine ist viel teurer.
The two jackets look the same, but one is much more expensive.