Online Geometry
Problem 621: Two Parallelograms, Diagonals, Centers,
Parallel Lines. Level: High School, Honors Geometry, College,
Mathematics Education

The figure shows two parallelograms ABCD and
ECFG with centers L, and H, respectively. E is on AB, and D on FG. EJ is
parallel to AD, and DK is parallel to GE. Prove that lines LH and KJ are
parallel.