lead / advantage
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lead
A spatial or temporal distance by which someone is ahead of someone else in a competition or movement.
Die Läuferin konnte ihren Vorsprung bis ins Ziel halten.
The runner was able to maintain her lead all the way to the finish.
The word is made up of 'vor' and 'Sprung'. So it literally describes a 'jump forward', which explains well the meaning of an advantage or a lead.
Durch die neue Technologie hat die Firma einen großen Vorsprung.
Thanks to the new technology, the company has a big advantage.
To say over whom or what someone has an advantage, the preposition 'vor' is used with the dative. The structure is: einen Vorsprung vor jemandem/etwas haben (to have a lead/advantage over someone/something).
Die Heimmannschaft hat einen Vorsprung von zwei Toren vor den Gästen.
The home team has a two-goal lead over the visitors.
In sports or competitive contexts, 'Vorsprung' (lead) is often combined with verbs like 'ausbauen' (to extend), 'verteidigen' (to defend/maintain), or 'verlieren' (to lose).
Der Radfahrer versucht, seinen Vorsprung auf den letzten Kilometern zu verteidigen.
The cyclist is trying to defend his lead over the final kilometers.
In the meaning of a protruding part, 'Vorsprung' (projection/ledge) is often used in compound words like 'Felsvorsprung' (rock ledge) or 'Mauervorsprung' (wall projection). This helps you recognize this meaning quickly.
Auf dem schmalen Felsvorsprung wuchsen einige seltene Pflanzen.
A few rare plants were growing on the narrow rock ledge.
leadership / tour / lead
'die Führung' and 'der Vorsprung' can both mean that someone is ahead in a competition or comparison. 'Führung' describes the position at the front: a team or person is currently first. 'Vorsprung' describes the gap to the others, for example two goals, ten seconds, or an advantage in knowledge. The words can be confused because they often occur together. In practical terms: 'Führung' says who is in front; 'Vorsprung' says how big the gap is.
Für die Prüfung hat Lena einen Vorsprung, weil sie schon früher gelernt hat.
Lena has an advantage for the exam because she started studying earlier.
Kurz vor der Pause übernimmt unsere Mannschaft die Führung.
Shortly before halftime, our team takes the lead.