Ruler and Compass Construction
Square Through Four Given Points

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1. Segment AC
2. Perpendicular to AC through B
3. Circle centered at B, radius AC
4. Line DE
5. Perpendiculr to DE through A
6. Perpendicular to FA through B
7. Perpendicular to GB through C
8. Square FGHI

Explanation of the construction:
Looking at the final configuration, one can see that the slant transversal distance AB
between lines FG and IH must be the same as the slant distance on the 90 degree
rotated transversal between lines FI and GH. So we construct the rotated transversal BE
and measure off distance AC to find point E.