Ruler and Compass Construction 4
Square Constructed On a Given Side

1. Extend AB
2. Circle centered at B, arbitrary radius
3. Two circles centered at E and F, same radius
4. Perpendicular ray BG
5. Circle centered at B, radius side of square
6. Circle centered at C, radius side of square
7. Circle centered at A, radius side of square
8. Sides AD, DC of the square
Why it works: The perpendicular bisector construction of G provides a right angle. Then marking off equal length sides provides a rhombus, which has a right angle, so it is a square.
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