So angle B= angle D=90 degrees.

OCF angle =45 degrees.

AB=AD=BC=DC

Because AE=AF

So the right triangle ABE and the right triangle ADF are congruent (HL)

So BE=DF

(2) The quadrilateral AEMF is a diamond.

Proof: because BC=BE+CE (proved)

DC=DF+CF (certification)

BE=DF (certification)

So CE=CF

Because angle OCE= angle OCF=45 degrees (proved)

OC=OC

So triangle OCE and triangle OCF are congruent (SAS)

So OE=OF

Angle COE= angle COF

Because angle COE+ angle COF= 180 degrees.

So angle COE= angle COF=90 degrees.

So EF is perpendicular to AM.

Because OM=AM

So AM and EF are equally divided. AM and EF are perpendicular to each other.

So the quadrilateral AEMF is a diamond.