Question

if c⊥b and a || c, what do you know about the relationship between lines a and b? justify your conclusion with a theorem or postulate.
o a⊥b, by the perpendicular transversal theorem
o a⊥b, by the alternate exterior angles theorem
o a || b, by the perpendicular transversal theorem
o not enough information

Explanation:

Step1: Recall relevant theorems

The Perpendicular Transversal Theorem states that if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. Here, line $b$ is a transversal to parallel lines $a$ and $c$ ($a\parallel c$) and $c\perp b$.

Step2: Apply the theorem

Since $a\parallel c$ and $c\perp b$, by the Perpendicular Transversal Theorem, $a\perp b$. The Alternate - Exterior Angles Theorem is about equal angles formed by a transversal with parallel lines and is not relevant here for determining perpendicularity.

Answer:

A. $a\perp b$, by the Perpendicular Transversal Theorem