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.
3
Define a translation from B to C. (Use menu item "Mode/Transformation/Translation" then select B as a peimage point and select C as an image point to generate the translation button [B to C].
4 Select the line AB and the two points A and B then press the translation button [B to C] to construct the image of the line AB by the defined translation.
5 Join up the four points A, B, C, and D to get the required parallelogram.
6 Switch to drag mode. Pick a free element. Move it around to check your construction.
Construction Theorems
If two sides of a quadrilateral are parallel and equal in length, then the quadrilateral is a parallelogram.

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