When two lines are parallel, all four angles formed by the intersection of the two lines are right angles, meaning their angle measures are (90°). This means that alternate interior angles are congruent because all alternate interior angles measures equal (90°). Therefore, by the alternate interior angles converse theorem, lines () and () are parallel.
The alternate interior angles converse theorem states if two angles are congruent and they have the relation of being a part of two lines intersected by a third line, then the two non-intersecting lines are parallel.
Step-by-step explanation: When two lines are parallel, all four angles formed by the intersection of the two lines are right angles, meaning their angle measures are (90°). This means that alternate interior angles are congruent because all alternate interior angles measures equal (90°). Therefore, by the alternate interior angles converse theorem, lines () and () are parallel.
The alternate interior angles converse theorem states if two angles are congruent and they have the relation of being a part of two lines intersected by a third line, then the two non-intersecting lines are parallel.
