Straightedge right-angle construction in a hexagon

ok, I am working on a math problem. I got the solution by making a right angle. However I am not allowed to do that because the contrains are that it must be done only with a straight-edge.

Let's say I have a Hexagon with vertices A and B opposing each other. How to I make a ray starting at B which is at an right angle to the ray AB? With proof please :D

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You can easily extend the triangular grid defined by the haxagon: Let $A,B,C,D,E,F$ be the vertices of the hexagon (I prefer these "logical" names, so your opposing vertices are $A,D$ instead of $A,B$).
Let $AF$ and $CE$ intersect in $G$, let $EF$ and $CD$ intersect in $H$. Let $GH$ and $BE$ intersect in $I$. Then $ID\perp AD$. The proof is straightforward as all points belong to the grid.