The Alternate Interior Angles theorem states that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles formed are congruent. These angles are formed on the opposite sides of the transversal and can be used to determine whether the given lines are parallel or not.
Alternate interior angles are pairs of non-adjacent angles located on opposite sides of the transversal and inside the two parallel lines. They are formed when a transversal intersects two parallel or non-parallel lines. These angles lie on the inner side of the parallel lines but on the opposite side of the transversal.
The alternate interior angles theorem states that when a transversal intersects two parallel lines, the resulting alternate interior angles are congruent. This is because the resulting alternate interior angles or alternate exterior angles are equal in measure.
In other words, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles formed are congruent. Conversely, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles formed are not congruent.
In summary, the Alternate Interior Angles theorem is a mathematical concept that states that when two parallel lines are cut by a transversal, the pairs of alternate interior angles formed are congruent. This theorem can be applied to various situations, such as when two parallel lines are cut by a transversal, and vice versa.
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