Alternate interior angles are not supplementary; they are actually congruent. This means that when two parallel lines are crossed by a transversal, the alternate interior angles formed are equal in measure.
To understand this concept better, consider two parallel lines, say line A and line B, being intersected by a transversal line C. The angles that lie on opposite sides of the transversal but inside the two parallel lines are called alternate interior angles. For example, if one alternate interior angle measures 30 degrees, the opposite alternate interior angle will also measure 30 degrees.
The reason for this congruence is based on the properties of parallel lines and transversals, as established by the Euclidean geometry principles. Thus, alternate interior angles maintain their equality and are vital in proving various geometric theorems, such as when solving for unknown angles in geometric problems.