Constructing a Rectangle with a Given Base

Construction Algorithm
1 Construct a line AB as a given base of the rectangle.
2 Construct a perpendicular line to AB through the point B.
3 Construct a point C on the perpendicular line.
4 Construct M as a midpoint of the diagonal AC.
5 Construct a circle centered at M and has a circumference point at B.
6 Construct the line that connects the two points B and M.
7 Generate the intersection point between the line BM and the circle at D.
8 Join up the four points A, B, C and D to get the required rectangle.
9 Switch to Move Mode. Pick a free element. Move it around to check your construction.
Construction Theorems
A rectangle is a parallelogram with a right angle.

A parallelogram is a quadrilateral, in which diagonals bisect each other.
Please enable Java for an interactive construction (with Cinderella).