18.106 Given a convex quadrilateral $ABCD$ where $AB \parallel CD$, and $AB + BC = CD + AD$. Then
(A) $AD > BC$.
(B) $AD < BC$.
(C) $AD = BC$.
(D) The size relationship between $AD$ and $BC$ cannot be determined.
(Chinese Jiangsu Province Junior High School Mathematics Competition, 1987)
［Solution］Assume $A D \times B C$, draw $C E / / A D$ intersecting $A B$ at $E$ (as shown in the figure), and since $A B / / C D$, then
$$
A E=C D, \quad C E=A D .
$$

From the given, $C D+A D=A B+B C$, we have
$$
A E+A D=A E+E B+B C,
$$

which simplifies to
$$
B E+B C=A D=E C \text {, which is not reasonable. }
$$

Therefore, $A D / / B C$, meaning quadrilateral $A B C D$ is a parallelogram.
$$
\therefore \quad A D=B C \text {. }
$$

Hence, the correct choice is $(C)$.