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 Construct a perpendicular line to AC through the point B.
5 Construct a circle centered at C and has radius AB.
6 Generate the intersection point between the constructed circle at C and the perpendicular line through B to get the fourth point of the rhombus D.
7 Join up the four points A, B, C, and D to get the required rhombus.
8 Switch to Move 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.

The two diagonals of a rhombus are perpendicular to each other.

Please enable Java for an interactive construction (with Cinderella).
Please enable Java for an interactive construction (with Cinderella).