Constructing a Square with a Given Diagonal

Construction Algorithm
1 Construct a line AC as a given diagonal of the square.
2 Construct M as a midpoint of the diagonal AC.
3 Construct the perpendicular line at M.
4 Construct a circle centered at M and has a radius MC.
5 Generate the intersection points between the circle and the perpendicular line at M to construct B and D.
6 Join up the four points A, B, C and D to get the required square.
7 Switch to Move Mode. Pick a free element. Move it around to check your construction.

Construction Theorem

The two diagonals of the square are perpendicular to each other and equal in length.

Please enable Java for an interactive construction (with Cinderella).
Please enable Java for an interactive construction (with Cinderella).