In this Desmos activity, students will use their knowledge of parallelograms to correctly find the location of a 4th vertex.

This learning resource provides students insight into combining and subdividing figures as well as utilizing the understanding of quadrilaterals.  Along with the exploration, students will be developing critical thinking through the decisions that are made to create the final mathematical product.  They will also communicate through collaboration to produce a final mathematical product.  They will also develop creative thinking and citizenship by producing a written piece to show their caring and understanding nature.

This is a reasonably direct task aimed at having students use previously-derived results to learn new facts about parallelograms, as opposed to deriving them from first principles. The solution provided (among other possibilities) uses the SAS trial congruence theorem, and the fact that opposite sides of parallelograms are congruent.