Question

1. if ( aparallel bparallel c ) and ( cperp d ), which of the following statements is (are) true?

i. ( aparallel c ) ii. ( aperp d ) iii. ( aperp b )
a. i only d. i and iii only
b. i and ii only e. i, ii, and iii
c. ii and iii only

Explanation:

Step1: Analyze statement I

If \(a\parallel b\) and \(b\parallel c\), then by the transitive property of parallel lines \(a\parallel c\).

Step2: Analyze statement II

Since \(a\parallel c\) and \(c\perp d\), if a line is parallel to another line and the second line is perpendicular to a third line, then the first line is also perpendicular to the third line. So \(a\perp d\).

Step3: Analyze statement III

Given \(a\parallel b\), parallel lines are not perpendicular (\(a\perp b\) would mean the angle between them is \(90^{\circ}\), but parallel lines have an angle of \(0^{\circ}\) between them). So \(a\parallel b\) implies \(a\) is not perpendicular to \(b\).

Answer:

b. I and II only