## Geometry: Common Core (15th Edition)

$a$ is perpendicular to $d$. or, $a \perp d$
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, $a \perp d$