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 Generate the intersection point between the perpendicular line through B and the line AC at M.
6 Construct a circle centered at M and has radius MB.
7 Generate the intersection between the circle and the perpendicular line through the point B at D.
8 Join up the four points A, B, C, and D to get the required rhombus.
9 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.

The two diagonals of a rhombus are perpendicular and bisect each other.

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