Constructing a Square with a Given Base

Construction Algorithm
1 Construct a line AB as a given base of the square.
2 Construct the perpendicular line at B.
3 Construct a circle centered at B and has a radius AB.
4 Generate the intersection point C between the circle and the perpendicular at B.
5 Construct the line that joins between A and C.
6 Construct the midpoint M between A and C.
7 Construct the line that joins between M and B.
8 Construct a circle centered at M and has MB as a radius.
9 Join up the four points A, B, C and D to get the required square.
10 Switch to drag mode. Pick a free element. Move it around to check your construction.

Construction Theorems

A square is a quadrilateral whose four right angles and four sides equal in length.

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).