2) Two parallelograms ABCD and DCEF are put together along their common side CD. Prove that the quadrilateral ABEF is also a parallelogram.
BTW it was number 2 in this link and was unanswered https://web2.0calc.com/questions/geometry-help_100
In parallelogram ABCD, AB = CD and AB || CD.
In parallelogram CDFE, DC = FE and DC || FE.
Therefore, AB = FE and AB || EF.
Since a pair of sides of quadrilater ABEF are both parallel and congruent, ABEF is a parallelogram.