3. The condition that can determine quadrilateral $ABCD$ is a rhombus is ( ).
(A) Diagonal $AC$ bisects diagonal $BD$, and $AC \perp$ $BD$
(B) Diagonal $AC$ bisects diagonal $BD$, and $\angle A=$ $\angle C$
(C) Diagonal $AC$ bisects diagonal $BD$, and bisects $\angle A, \angle C$
(D) Diagonal $AC$ bisects $\angle A, \angle C$, and $\angle A=$ $\angle C$
3. D.

As shown in Figure 4, $AC$ bisects $BD$, $AC \perp BD$, and $AC$ also bisects $\angle A$ and $\angle C$, so we can rule out options (A) and (C). Option (B)’s condition can only lead to the conclusion that quadrilateral $ABCD$ is a parallelogram, hence we exclude option (B).