Constructing a Square with a Given Base

Construction Algorithm
1 Construct a line AB as a given base of the square.
2 Construct a line at B so that it makes an angle 135° (measured anti-clockwise) with the base AB.
3 Construct another line at A so that it makes an angle 45°(measured anti-clockwise) with the base AB.
4 Generate the intersection point between the two constructed lines in steps 2 and 3 at M.
5 The rotation button is already generated in the construction area.
6 Rotate the point B by the defined rotation to construct the vertex C, then rotate the point C to get the fourth vertex D of the square.
7 Join up the four points A, B, C and D to get the required square.
8 Switch to drag mode. Pick a free element. Move it around to check your construction.

Construction Theorems

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

Each diagonal of the square bisects two opposite angles.

Rotation preserves the distance between points.

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