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.
congruent
In geometry, the property of two or more figures that match exactly in shape and size and can therefore be placed perfectly on top of each other (congruent).
Wenn alle drei Seitenlängen übereinstimmen, sind die beiden Dreiecke deckungsgleich.
If all three side lengths match, the two triangles are congruent.
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.
identical
For figures, identisch and deckungsgleich can both express complete agreement. Identisch emphasizes that all characteristics are the same, whereas deckungsgleich specifically means that the figures can be placed exactly on top of each other. For geometric shapes, deckungsgleich is therefore usually the more precise choice.
Die beiden Dreiecke sind deckungsgleich und lassen sich genau übereinanderlegen.
The two triangles are congruent and can be placed exactly on top of each other.
Die beiden ausgeschnittenen Sterne sind in Form, Größe und Farbe identisch.
The two cut-out stars are identical in shape, size, and color.
