It is known that in the quadrilateral ABCD, ab = DC, e and F are the midpoint of AD and BC respectively, GH ⊥ EF intersects AB and DC at g, h and O respectively, which are perpendicular feet It is known that in the quadrilateral ABCD, ab = DC, e and F are the midpoint of AD and BC respectively, GH ⊥ EF intersects AB and DC at g, h and O respectively, which are perpendicular feet

It is known that in the quadrilateral ABCD, ab = DC, e and F are the midpoint of AD and BC respectively, GH ⊥ EF intersects AB and DC at g, h and O respectively, which are perpendicular feet It is known that in the quadrilateral ABCD, ab = DC, e and F are the midpoint of AD and BC respectively, GH ⊥ EF intersects AB and DC at g, h and O respectively, which are perpendicular feet

It is proved that extending Fe intersects Ba and CD at P and Q respectively, takes AC midpoint m, connects EM and FM, because e is the midpoint of AD and M is AC midpoint, EM is the median line of △ ABC, so EM = AB / 2 and me / / AB is the same as FM = CD / 2 and MF / / CD, because AB = CD, me = MF, so ∠ MEF = MFE, because me / / AB, so ∠ ape = ∠ MEF