Constructing a Rhombus with a Given Base

Construction Algorithm
1 Construct a line AB as a given base of the rhombus.
2 Construct the line BC so that AB = BC.
3 Define a translation from B to C. (Use menu item "Mode/Transformation/Translation" then select B as a peimage point and select C as an image point to generate the translation button [B to C].
4 Select the line AB and the two points A and B as well then press the translation button [B to C] to construct the image of the line AB by the defined translation.
5 Join up the four points A, B, C and D 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.

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