The paper in the shape of an isosceles right triangle ABC shown in the figure is folded along [AD] so that side $AB$ falls onto side $AC$.
Accordingly, what is the ratio $\frac { | C D | } { | A B | }$?
A) $\frac { 1 } { 2 }$
B) $\frac { 2 } { 3 }$
C) $\frac { \sqrt { 2 } } { 2 }$
D) $2 - \sqrt { 2 }$
E) $3 - 2 \sqrt { 2 }$