Question

if (cperp b) and (aparallel c), what do you know about the relationship between lines (a) and (b)? justify your conclusion with a theorem or postulate.

(aperp b) by the alternate exterior angles theorem
(aparallel b) by the perpendicular transversal theorem
not enough information
(aperp b) by the perpendicular transversal theorem

Explanation:

Step1: Recall line - relationship theorems

Given \(c\perp b\) means the angle between \(c\) and \(b\) is \(90^{\circ}\), and \(a\parallel c\).

Step2: Apply the Perpendicular Transversal Theorem

If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other. Since \(c\perp b\) and \(a\parallel c\), we can conclude that \(a\perp b\).

Answer:

a⊥b by the Perpendicular Transversal Theorem