$△ABC$ and $△ABD$ are on a common base $AB$, with $AC=BD$ and $BC=AD$. Which of the following options is true?

In $△ABC$ and $△BAD$:$AB=BA$ (Common side)$BC=AD$ (Given)$AC=BD$ (Given)By SSS (Side-Side-Side) congruence criterion:
$$△ABC\cong △BAD$$
The correspondence of vertices must be written in the correct order: $A\leftrightarrow B$, $B\leftrightarrow A$, and $C\leftrightarrow D$. Therefore, $△ABC\cong △BAD$ is the correct statement.