3. Given a convex quadrilateral $A B C D$ where $A D / / B C$, and $A B+B C=C D+A D$. Then the size relationship between $A D$ and $B C$ is ( ).
(A) $A D>B C$
(B) $A D<B C$
(C) $A D=B C$
(D) Any of the above three situations is possible
3.C.

As shown in Figure 3, draw a line through $C$ parallel to $AB$, intersecting the extension of $AD$ at $E$. Then, quadrilateral $ABCE$ is a parallelogram. Therefore,
$$
A B+B C=C E+A E .
$$

Since $A B+B C=C D+A D$, we have
$$
C E+A E=C D+A D \text {. }
$$

Thus, $D$ must coincide with $E$, meaning quadrilateral $ABCD$ is a parallelogram, and $A D=B C$.