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.