So BC=2ED angle AED=ABC, so ED is parallel to BC.
Similarly, the triangle GMN is similar to GBC, and BC=2MN MN is parallel to BC.
To sum up, BC=2ED BC=2MN is ED=MN.
ED is parallel to BC and MN is parallel to BC, that is, ED is parallel to Mn.
So EDNM is a parallelogram.