Question

each tie on the railroad tracks is perpendicular to both of the tracks. what is the relationship between the two tracks? justify your answer. the two tracks are perpendicular by the perpendicular transversal theorem. the two tracks are parallel by the converse of the perpendicular transversal theorem. the two tracks are parallel by the same - side interior angles postulate. the two tracks are perpendicular by the definition of complementary angles.

Explanation:

Step1: Recall relevant geometric theorems

The perpendicular transversal theorem states that if a transversal is perpendicular to one of two parallel lines, it is perpendicular to the other. The converse is also true. Here, the railroad - ties act as transversals and are perpendicular to both tracks.

Step2: Apply the converse of the perpendicular transversal theorem

Since each tie (transversal) is perpendicular to both tracks, by the converse of the perpendicular transversal theorem, the two tracks are parallel.

Answer:

The two tracks are parallel by the Converse of the Perpendicular Transversal Theorem.