Constructing a Parallelogram with a Given Base

Construction Algorithm
1 Construct a line AB as a given base of the parallelogram.
2 Construct a point C above the line AB and the line joining B and C.
3 Construct a circle centered at A and has a radius BC.
4 Construct another circle centered at C and has a radius AB.
5 Generate the intersection point between the two circles to find the vertex D of the parallelogram.
6 Construct the two lines CD and AD.
7 Join up the four points A, B, C and D to get the required parallelogram.
8 Switch to drag mode. Pick a free element. Move it around to check your construction.

Construction Theorem

A parallelogram is a quadrilateral, in which each two opposite sides are equal in length.

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