Final answer:
In a parallelogram, alternate interior angles are equal due to the properties of parallel lines being crossed by a transversal.
Step-by-step explanation:
In a parallelogram, alternate interior angles are equal. This is because when two parallel lines are cut by a transversal, the pairs of angles on opposite sides of the transversal but inside the two lines are equal.
In the case of a parallelogram, the opposite sides are parallel, and the consecutive angles form alternate interior angles with the transversal that cuts through them. Hence, these angles are always equal.
In a parallelogram, the alternate interior angles are congruent, or equal in measure.
This means that if we have two parallel lines intersected by a transversal, the alternate interior angles formed between the two parallel lines will be equal.
For example, in parallelogram ABCD, angle A and angle C are alternate interior angles and they are congruent.