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Use only a non-collapsible compass and a straight-edge (not a ruler), construct a square with sides AB.
1. Have the compass length as AB.
2. Draw a straight line XY with a straight edge of length much greater than AB.
3. Now mark a point P on XY.
4. With P as center cut an arc on line XY for Q. Now PQ = AB.
5. With P as center cut two arcs on either side of line XY.
6. 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.
7. Mark those points as R and S.
8. Now join P, R, Q, S.
9. Now we have a parallelogram PRQS. PR = RQ = QS = SP parallelogram with all sides equal is a rhombus.
10. The Diagonals of the rhombus are perpendicular to each other
11. Now Draw a line UV with points R ans S.
12. Now mark the point at which RS cuts PQ as A.
13. With A as center cut an arc on UV to get the point C.
14. With A as center cut an arc on XY to get the point B.
15. With B as center cut an arc on one side of XY.
16. With C as center cut an arc which cuts the ac drawn with B as center to get the point D.
17. Now ABCD is the required Square with side AB.
use compass and ruler
Draw a line from the left side of your paper to the right using a ruler. Draw and label two endpoints. End point A will be on the left and end point B on the right. The distance from point A and point B will be labeled r. Distance r will be the length of each side of your square. Extend the line further to the right from point B to help in finding a new line that will be perpendicular to Line AB.
Draw a perpendicular line upwards from point B. Using distance r, mark and label a new end point C. This will be the second side of the square at an exact 90 degree angle.
Draw an arc with end point A as the center and r as the distance using a compass. Draw a second arc using end point C as the center and r as the distance. Mark and label where these two arcs meet as point D. This is the final corner for your square.
Connect end point A to point D with your ruler. Connect end point C to point D.