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 Construct the diagonal AC.
4 Define a reflection whose mirror AC. (Use the menu item "Modes/Transformation /Reflection" then select AC as a mirror).
5 Construct the image of the elements B, a, b by reflection on AC by selecting the point B and the two lines a and b then click on the reflection button defined in step 4.
6 Join up the four points to get the required rhombus.
7 Switch to drag mode. Pick a free element. Move it around to check your construction.
Construction Theorems
A rhombus is a quadrilateral with four equal sides.

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