
vorgeben
to pretend
To act as if something were the case; to feign or simulate something that is not true.
Er gab vor, krank zu sein, um nicht zur Arbeit gehen zu müssen.
He pretended to be sick so he wouldn't have to go to work.
to pretend / specify
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to pretend
To act as if something were the case; to feign or simulate something that is not true.
Er gab vor, krank zu sein, um nicht zur Arbeit gehen zu müssen.
He pretended to be sick so he wouldn't have to go to work.

to specify
To set or determine something as a rule, guideline, or goal. It defines a standard that is meant to be followed.
Die Architektin hat die genauen Maße für das Fundament vorgegeben.
The architect specified the exact measurements for the foundation.

to give a handicap
In a competition or game, to grant a weaker opponent an advantage, for example a head start or a playing piece.
Beim Schachspiel gab sie ihrem jüngeren Bruder einen Bauern vor.
In the chess game, she gave her younger brother a pawn as a handicap.
'Vorgeben' (to pretend / specify) is a separable verb. In a main clause, the prefix 'vor' comes at the end; in a subordinate clause, the verb stays together; and in the infinitive with 'zu', 'zu' comes between 'vor' and 'geben'.
Er gibt eine Erklärung vor.
He specifies an explanation.
You can recognize the meaning from context: If it is about deception, 'vortäuschen' (to pretend/feign) is meant. If it is about rules or goals, 'festlegen' (to set/specify) is meant. If it occurs in the context of a game, it often means 'einen Vorteil gewähren' (to grant an advantage).
Sie gab vor, müde zu sein, um gehen zu können.
She pretended to be tired so she could leave.
In the meaning 'vortäuschen' (to pretend/feign), 'vorgeben' is very often used with an infinitive construction with 'zu' or a 'dass' clause. This construction describes what the person is pretending to be or do.
Das Kind gab vor, zu schlafen.
The child pretended to be sleeping.
When 'vorgeben' means 'festlegen' (to set/specify), it is often combined with abstract concepts. Typical phrases are: 'die Richtung vorgeben' (to set the direction), 'ein Ziel vorgeben' (to set a goal), 'den Rahmen vorgeben' (to set the framework), or 'den Takt vorgeben' (to set the pace).
Die Regierung gibt die politische Richtung für die nächsten Jahre vor.
The government sets the political direction for the coming years.
In the meaning 'einen Vorteil gewähren' (to grant an advantage), the person who receives the advantage is in the dative. The pattern is: jemandem (dative) etwas (accusative) vorgeben.
Der erfahrene Spieler gab seinem Gegner eine Figur vor.
The experienced player gave his opponent a piece as a handicap.
to state / boast / report
Angeben is used when someone signals the pace, rhythm, or direction through their actions. Vorgeben emphasizes more strongly that a pace is established as a goal, rule, or binding standard. Thus, a leading person gives the pace, while a plan specifies it.

Beim gemeinsamen Lauf gibt der Trainingsplan ein festes Tempo vor.
During the group run, the training plan specifies a fixed pace.
Beim gemeinsamen Lauf gibt die erfahrene Läuferin das Tempo an.
During the group run, the experienced runner sets the pace.