Lines ℓ and m are intersected by transversal t and ℓ ∥ m.

The investiture controversy began as a power struggle between pope gregory vii (1072–85) and henry iv, holy roman emperor (1056–1106).[2] a brief but significant struggle over investiture also occurred between henry i of england and pope paschal ii in the years 1103 to 1107, and the issue played a minor role in the struggles between church and state in france, as well.by undercutting the imperial power established by the salian emperors, the controversy led to nearly 50 years of civil war in germany, and the triumph of the great dukes and abbots. imperial power was finally re-established under the hohenstaufen dynasty. historian norman cantor: