Question

1. what happens when alternate interior angles are congruent between two lines cut by a transversal?

lines are parallel
lines are skew
lines intersect
lines are perpendicular

Explanation:

When two lines are cut by a transversal, if the alternate interior angles are congruent, it is a fundamental property in geometry (specifically in the study of parallel lines and transversals) that the two lines are parallel. Skew lines are non - coplanar and not relevant here. Intersecting lines would not have congruent alternate interior angles in a general case (unless in a very specific non - parallel intersecting case which is not the rule). Perpendicular lines are a special case of intersecting lines (where the angle between them is \(90^{\circ}\)) and do not follow from the congruence of alternate interior angles.

Answer:

Lines are parallel