Parallel lines theorem and Perpendicular lines thereom

Parallel lines theorem [par-uh-lel lahyns thee-er-uhm]
Two lines are parallel if they're intersected by a transversal in such way that:

• The corresponding angles are congruent.
• The alternate interior angles are congruent.
• The alternate exterior angles are congruent.
• The same-side interior angles are supplementary (have a sum of 180 degrees).
• The same-side exterior angles are supplementary (have a sum of 180 degrees).

Perpendicular lines theorem [pur-puh-n-dik-yuh-ler lahyns thee-er-uhm]
Given a line (line 1) and a point that's not located on that exact line, there is one and only one line through the given point that is perpendicular to the given line (line 1).