Because triangle ACB and triangle ECD are isosceles right triangles,

So CE=CD, AC=BC, angle ECD= angle ACB=90 degrees,

So angle ACE= angle BCD,

So the triangle ACE is equal to the triangle BCD(S, a, s),

So AE=BD, angle EAC= angle DBC,

Because angle EAC+ angle CAD= 180 degrees,

So angle DBC+ angle CAD= 180 degrees,

Because the angle DBC+ angle EAD+ angle ACB+ angle ADB=360 degrees (the sum of the internal angles of the quadrilateral is equal to 360 degrees),

Angle ACB=90 degrees,

So the angle ADB=90 degrees,

So AE 2+AD 2 = BD 2+AD 2 = AB 2,

Because triangle ABC is an isosceles right triangle,

So ab 2 = AC 2+BC 2 = 2ac 2,

So AE 2+ad 2 = 2ac 2.