At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I'm not good with constructions, but you could construct two perpendicular lines at the end points of line AB, then use your compass to make sure those two lines were the same length as AB, then connect them with the fourth side. But your explanation probably needs to be more step-by-step...
Nice Question, i liked it. Made me think a bit and recollect my maths knowledge. Have the compass length as AB. Draw a straight line XY with a straight edge of length much greater than AB. Now mark a point P on XY. With P as center cut an arc on line XY for Q. Now PQ = AB. With P as center cut two arcs on either side of line XY. With Q as center cut two arcs on either side of line XY, so that they make two points with the arcs drawn with P as center. Mark those points as R and S. Now join P, R, Q, S. Now we have a paralleogram PRQS. PR = RQ = QS = SP parallelogram with all sides equal is a rhombus. The Diagonals of the rhombus are perpendicular to each other Now Draw a line UV with points R ans S. Now mark the point at which RS cuts PQ as A. With A as center cut an arc on UV to get the point C. With A as center cut an arc on XY to get the point B. With B as center cut an arc on one side of XY. With C as center cut an arc which cuts the ac drawn with B as center to get the point D. Now ABCD is the required Square with side AB.
yeah i think it needs to be like exactaly step by step..