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 M above the line AB.
3 Define a reflection at the point M, then construct the images of the two points A and B by reflection on M by selecting them to get the other two vertices of the parallelogram C and D.
4 Join up the four points A, B, C and D to get the required parallelogram.
5 Switch to drag mode. Pick a free element. Move it around to check your construction.

Construction Theorems

A parallelogram is a quadrilateral, in which diagonals bisect each other.

Reflection preserves the distance between points.

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