reversed / conversely
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reversed
In the opposite direction, order, or manner; the other way around.
Bitte lesen Sie die Zahlen in umgekehrter Reihenfolge vor, also von hinten nach vorne.
Please read the numbers aloud in reverse order, that is, from back to front.
'Umgekehrt' (reversed / conversely) is the past participle of the separable verb 'umkehren' (to turn around / to go back). This verb means to change direction and go back or to put something into the opposite position.
Auf halbem Weg merkten wir, dass wir etwas vergessen hatten, und kehrten um.
Halfway there, we realized that we had forgotten something and turned back.
The combination 'und umgekehrt' (and vice versa) is a very common fixed expression. It means something like 'and the other way around' or 'and vice versa'.
Ich helfe dir bei der Gartenarbeit und du hilfst mir beim Streichen, und umgekehrt.
I help you with the gardening and you help me with painting, and vice versa.
As an adjective, 'umgekehrt' (reversed) often describes abstract nouns such as 'Reihenfolge' (order), 'Richtung' (direction), 'Logik' (logic), or 'Fall' (case).
Im umgekehrten Fall, also wenn du zuerst kommst, ruf mich bitte an.
In the opposite case, that is, if you arrive first, please call me.
When 'umgekehrt' (conversely) stands at the beginning of a sentence to express a contrast, the conjugated verb follows directly after it (inversion).
Ich mag den Winter sehr. Umgekehrt hasst mein Bruder die Kälte.
I really like winter. Conversely, my brother hates the cold.
against it / however
'dagegen' and 'umgekehrt' can both express a contrast. You use 'dagegen' when someone is against something or when you compare two things: one thing is like this, while the other is different by contrast. 'umgekehrt' is closer to 'the other way around': the direction, order, or point of view is changed. The words can be confused because both show a contrast. When it is about objection or comparison, 'dagegen' often fits. When two sides or directions are swapped, 'umgekehrt' is more natural.
Wir helfen heute den Nachbarn; morgen ist es vielleicht umgekehrt.
We are helping the neighbors today; tomorrow it may be the other way around.
Sie möchte den Plan ändern, ihr Bruder ist dagegen.
She wants to change the plan; her brother is against it.