Answer
$a$ is perpendicular to $d$. or, $a \perp d$
Work Step by Step
We are given that $b \perp c$ , thus according to definition of perpendicular lines, we have: $m \angle 2 =90$
We are given that $a \parallel c$ , thus according to corresponding angles postulate, we have: $m (\angle 1) =m (\angle 2)$
We are given that $c \parallel d$ , thus according to corresponding angles postulate, we have: $m (\angle 3) =m (\angle 1)$
We need to use transitive property of equality.
This implies that $m (\angle 3) =m (\angle 1)=m (\angle 2)=90$
According to definition of perpendicular lines, we have: $m (\angle 3) =90$
So, $a$ is perpendicular to $d$. or, $a \perp d$
