Construct with a ruler and compass a square, given one point from each side.
I was reading the answer to Square Deal, and I do not understand how the rest is easy to solve. Could someone help me understand? I don't see the square.
Connect $A$ and $C$ and draw a perpendicular from $B$ to this segment. Now construct $D’$ on this perpendicular such that $AC = BD’$. $DD'$ is one side of the square. (This construction is already given in the link provided)
Now to complete the square, draw perpendiculars from point $A$ and $C$ to the line $DD'$. And then draw a line passing though $B$ parallel to $DD'$.