2. In Rt $\triangle A B C$, the lengths of the two legs $A B$ and $A C$ are 1 cm and 2 cm, respectively. Then, the length of the angle bisector of the right angle is equal to cm.
2. As shown in the figure, $A D$ is the angle bisector of the right angle $A$, and a line through $B$ parallel to $D A$ intersects the extension of $C A$ at point $E$. Then $\angle E B A=$
$$
\begin{aligned}
\angle B A D & =45^{\circ}, \\
A E & =A B=1, \\
E B & =\sqrt{2} .
\end{aligned}
$$
$$
\begin{array}{l}
\text { Also } \triangle C D A \backsim \triangle C B E, \\
\frac{A D}{E B}=\frac{A C}{C E}=\frac{2}{3}, \\
\therefore A D=\frac{2}{3} E B=\frac{2 \sqrt{2}}{3} .
\end{array}
$$