Same side interior angles are formed when a transversal crosses two parallel lines. These angles are located on the same side of the transversal and between the two lines. According to the properties of parallel lines and transversals, same side interior angles are not congruent; instead, they are supplementary, meaning that their measures add up to 180 degrees.
To understand why this is the case, consider two parallel lines cut by a transversal. The angle formed on one side of the transversal and the corresponding angle on the other line are both interior angles, but they are not equal. Instead, each same side interior angle, when added together, equals a straight line, hence they are supplementary.
This concept is crucial in geometry because it helps us establish relationships between angles formed by the interaction of parallel lines with a transversal. The non-congruence of same side interior angles supports various geometric proofs and is indexed in the properties of parallel lines, thereby providing a solid foundation for further advanced studies.