6. Given a convex quadrilateral $A B C D$ with $D C / / A B, A C$ $\perp B D$. Then ( ).
(A) $A B+D C < A D+B C$
6. B.
(1) When $D C \neq A B$, as shown in Figure 5(a), quadrilateral $A B C D$ is a trapezoid. Draw the midline $M N$. It is easy to see that
$$
A B+D C=2 M N \text {. }
$$

And $A D=2 P M, B C=2 P N(P$ is the intersection of $A C$ and $B D$), at this time,
$$
\begin{array}{l}
A B+D C=2 M N \\
<2(P M+P N)=A D+B C .
\end{array}
$$
(2) When $D C=A B$, as shown in Figure $5(\mathrm{~b})$, quadrilateral $A B C D$ is a rhombus. Clearly, $A B+D C=A D+B C$.