1. **Stating the problem:** We have a quadrilateral $ABCD$ with $AB \parallel CD$ and $\angle ADC = 90^\circ$. We need to determine which two statements among A, B, C, and D must be true. 2. **Given information:** - $AB \parallel CD$ means $AB$ and $CD$ are parallel lines. - $\angle ADC = 90^\circ$ means the angle at vertex $D$ between points $A$ and $C$ is a right angle. 3. **Analyzing each statement:** - **A: $m\angle DAB = 90^\circ$** Since $AB \parallel CD$ and $AD$ is a transversal, $\angle ADC = 90^\circ$ implies $\angle DAB$ is also $90^\circ$ by the property of alternate interior angles between parallel lines. - **B: $m\angle ABC = 90^\circ$** There is no information to conclude $\angle ABC$ is $90^\circ$. - **C: $\angle DAC \cong \angle BCA$** These angles are not necessarily congruent based on the given information. - **D: $\angle ABD \cong \angle CDB$** Since $AB \parallel CD$ and $BD$ is a transversal, $\angle ABD$ and $\angle CDB$ are alternate interior angles and thus congruent. 4. **Conclusion:** The two statements that must be true are **A** and **D**. Final answer: **A and D**.