Ruler and Compass Construction 30
Square Through Four Given Points

1. Segment AC
2. Perpendicular to AC through B
3. Arc centered at B, radius AC; intersection E
4. Line DE
5. Perpendicular to DE through A; intersection F
6. Perpendicular to FA through B; intersection G
7. Perpendicular to GB through C; intersections H,I
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.
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