So AB=AD=DC

Angle BAE= Angle ADF=90 degrees.

Because AD=AE+DE

DC=DF+CF

DE=CF

So AE=DF

So triangle ABE and triangle DFA are congruent (SAS)

So angle AEO= angle AFD

Because angle DAF+ angle ADF+ angle AFD= 180 degrees.

So DAF angle +AEO angle =90 degrees.

Because DAF angle +AEO angle +AOE angle = 180 degrees.

So AOE angle =90 degrees

So vertical AF.

(2) Solution: Because DG is perpendicular to AF.

So OGD angle =90 degrees.

Because angle AOE+ angle EOG= 180 degrees

So EOG angle =90 degrees

Because EH vertical DG

So EHG angle =90 degrees

Because OGD angle +EOG angle +EHG angle +OEH angle =360 degrees.

So OEH angle =90 degrees.

So OEH angle = EOG angle = OGD angle = EHG angle =90 degrees.

So the quadrilateral is a rectangle.

So OG=EH

EH parallel autofocus

So angel ·DEH = angel ·DAF

Angle ADF= Angle EHD=90 degrees.

So the triangle ADF is similar to the triangle EHD (AA).

So EH/DE=DF/AF=4/5.

Because OG/DE=4/5

So EH/DE=4/5.

In the right triangle ADF, the angle ADF=90 degrees.

From Pythagorean Theorem:

AF^2=AD^2+DF^2

So DF/AD=3/4.

Because AD=4

So DF=3

Because the side length of a square is 4.

So: AD=DC=4

DC=DF+CF=4

So CF=4-3= 1.

Because DE=CF

So DE= 1