Constructing a Rhombus with a Given Base

Construction Algorithm
1 Construct a line AB as a given base of the rhombus.
2 Construct a line BC so that AB = BC considering that C is the third vertex of the rhombus.
3 Construct the diagonal AC.
4 Switch to Mirror Mode. Define a reflection at the diagonal AC, then construct the image of the point B by reflection on AC to get the fourth vertex D.
5 Join up the four points to get the required rhombus.
6 Switch to drag mode. Pick a free element. Move it around to check your construction.
Construction Theorems
A rhombus is a parallelogram in which two adjacent sides are equal in length and the diagonals are perpendicular to each other.

Reflection preserves the distance between points.
Please enable Java for an interactive construction (with Cinderella).