The Perpendicular Transversal Theorem is a mathematically proven statement that governs a line that passes through two lines at two separate points and in the same geometric plane. The theorem states that if a line traverses perpendicularly to the first of two parallel lines, then it is also perpendicular to the second line.
The Perpendicular Transversal Theorem belongs to a whole class of theorems in Geometry. Its main focal point is the transversal, which is defined as any line that intersects two other lines at two separate and distinct points within the same plane. In this particular theorem, the situation is special in the sense that the two lines where the transversal passes through are parallel to each other.
This theorem may be used to support Euclid's parallel postulate, which involves finding proof of the parallel nature of two lines. It is also a special case of the Alternate Interior Angles Theorem, which states that if a line cuts through two parallel lines, then the alternate interior angles are congruent. In the case of the Perpendicular Transversal Theorem, the alternate interior angles are all at 90 degrees.
The theorem deals with transversals, which involve not only on perpendicular angles but also any other angular measurement. Transversals are one of the main topics of discussion in Euclid's parallel postulate.