Question

guided practice
look at the figure.
if ( a perp b ) and ( b parallel c ), which of the following must be true?
a. ( b perp c )
b. ( a parallel c )
c. ( a perp c )
d. ( a parallel b )
parallel and perpendicular

Explanation:

Step1: Recall the property of perpendicular and parallel lines

If a line \(a\perp b\) and \(b\parallel c\), then by the property that if a line is perpendicular to one of two parallel lines, it is perpendicular to the other.

Step2: Analyze each option

• Option A: \(b\perp c\) is wrong because \(b\parallel c\) (given).
• Option B: \(a\parallel c\) is wrong.
• Option C: Since \(a\perp b\) and \(b\parallel c\), then \(a\perp c\) (by the property of perpendicular - parallel lines).
• Option D: \(a\parallel b\) is wrong as \(a\perp b\) (given).

Answer:

C. \(a\perp c\)