Final answer:
Same Side Interior angles being congruent indicates the lines are perpendicular, not parallel because such angles would each be 90 degrees.
Step-by-step explanation:
If the Same Side Interior angles are congruent, this does not necessarily make the lines parallel. In geometry, when two lines are crossed by a transversal, the same side interior angles are the pair of angles that lie between the two lines and on the same side of the transversal.
According to the Parallel Postulate, if two lines are cut by a transversal and the same side interior angles are supplementary (add up to 180 degrees), then the lines are parallel. However, if the same side interior angles are congruent, this would imply each angle is 90 degrees, making the lines perpendicular, not parallel.
When the Same Side Interior angles are congruent, it does not necessarily mean that the lines are parallel. Same Side Interior angles are the angles formed by two lines crossed by a transversal on the same side of the transversal.
These angles are congruent only when the lines crossed by the transversal are parallel. If the lines are not parallel, the Same Side Interior angles will not be congruent.
For example, consider two lines crossed by a transversal.