When parallel lines are cut by a transversal, why are the measures of corresponding angles equal? because parallel lines always have identical y–intercepts, so a transversal will always intersect parallel lines in the same way because parallel lines always have identical slopes, so a transversal will always intersect parallel lines in the same way because transversals always have identical y–intercepts, so a transversal will always intersect parallel lines in the same way because transversals always have identical slopes, so a transversal will always intersect parallel lines in the same way