233. All edges of a regular triangular prism $A B C A_{1} B_{1} C_{1}$ have length $a$. Segments with endpoints on the diagonals $B C_{1}$ and $C A_{1}$ of the lateral faces, parallel to the plane $A B B_{1} A_{1}$, are considered. Find the smallest length of such segments.
233. If a plane, drawn through our segment parallel to the face $A B B_{1} A_{1}$, intersects $C B$ at point $K$ such that $|C K|=x$, then the projection of the segment on the face $A B C$ has a length of $x$, and its projection on the edge $C C_{\mathbf{1}}$ is $|a-2 x|$; thus, the length of the segment will be

$$
\sqrt{x^{2}+(a-2 x)^{2}}=\sqrt{5 x^{2}-4 a x+a^{2}}
$$

The smallest length is $\frac{a}{\sqrt{5}}$.