Question

if a//b and b//c and c⊥d, then
a. a⊥b
b. a//e
c. a⊥d
d. a//d

Explanation:

Step1: Analyze Parallel and Perpendicular Rules

Given \( a \parallel b \) and \( b \parallel c \), by the transitive property of parallel lines, \( a \parallel c \). Then, since \( c \perp d \), if a line is parallel to a line perpendicular to another line, it is also perpendicular to that line. So \( a \perp d \) (because \( a \parallel c \) and \( c \perp d \), so \( a \) inherits the perpendicularity to \( d \)).

Step2: Evaluate Each Option

• Option A: \( a \perp b \) is false because \( a \parallel b \).
• Option B: \( a \parallel e \) – no info about \( e \), so can't conclude.
• Option C: \( a \perp d \) matches our deduction.
• Option D: \( a \parallel d \) is false as we found \( a \perp d \).

Answer:

C. \( a \perp d \)