So AG=AE

Angle EAG=90 degrees

Because the quadrilateral ABCD is a square

So AB=AD

Angle error =90 degrees

Angle DAC=45 degrees

Because DAG= EAG+ DAE=90+ DAE.

BAE= BAD+ DAE=90+ DAE。

So angle DAG= angle BAE

So triangle DAG and triangle BAE are congruent (SAS)

So angle AGM= angle AEH

Because angle AGM+ angle EAG+ angle AMG= 180 degrees.

So angle AGM+ angle AMG=90 degrees.

Because angle AMG= angle HME

So AEH angle +HME angle =90 degrees.

Because angle HME+ angle AEM+ angle MHE= 180 degrees.

So MHE angle =90 degrees

So EB is perpendicular to GD.

(2) It is proved that the intersection D makes DN perpendicular to AC in n..

So angle DNA= angle DNG=90 degrees.

Because the angle DAC=45 degrees

Angle DAC+ angle ADN+ angle DNA= 180 degrees.

So the angle ADN=45 degrees

So angle ADN= angle DAC=45 degrees.

So DN=AN

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

So DG 2 = DN 2+NG 2.

Tangent angle AGH=DN/NG=3/4.

NG=AG+AN

AG= root number 2

So DG=5 times the root number 2.

Because triangle DAG and triangle BAE are congruent (proved)

So DG=EB

So EB=5 times the root number 2.