The quadrilateral ABCD is a diamond. The extension of de perpendicular to ab intersects BA at point E, and DF perpendicular to BC intersects BC at point F. please guess the size of De and DF

The quadrilateral ABCD is a diamond. The extension of de perpendicular to ab intersects BA at point E, and DF perpendicular to BC intersects BC at point F. please guess the size of De and DF

De and DF are of equal length, which is proved as follows
If the parallel line of de through a intersects DC at n, then ∠ ANC is a right angle
If the parallel line of DF passes through C and intersects ad at m, then ∠ CMD is a right angle
Because ABCD is diamond, ad = DC
If the area of triangle ADC is 0.5 * ad * cm = 0.5 * DC * an, then cm = an
Because ad ‖ BC, CM = DF, similarly an = De
So de = DF