In this diagram, which equation could you prove to be true in order to conclude that the lines are parallel?

−ab=−cd

−ab⋅−dc=−1

−ab⋅−cd=−1

−ab=−dc

I believe there is something wrong with the fourth equation. It shouldn"t be equal the first equation. It should be: -ac = - db

Let's calculate the linear equations of AB & CD
x/(x-b) = (y-a)/y
xy = (x-b)(y-a)
-ax-by+ab=0
y=-ax/b+a

(x+c)/x= y/(y+d)
(x+c)(y+d)=xy
dx+cy+cd=0
y=-dx/c - d

-a/b = -d/c in other words:
-ac = -db (Resembling the fourth equation)

Idk idk idk idk idk idk idk idk