Answer:
AD ≅ BC | Given
AD || BC | Given
∠CAD ≅ ∠ACB | Alternate Interior Angles Theorem
AC ≅ AC | Reflexive Property of Congruence
△ABC ≅ △CDA | SAS Theorem
Explanation:
Since we know that AD and BC are parallel (given), we can think of the diagonal AC as a transversal to these parallel lines.
So, we can use the Alternate Interior Angles Theorem, which states that alternate interior angles are congruent. Hence, ∠CAD ≅ ∠ACB.
We also know that AC ≅ AC because of the Reflexive Property of Congruence.
Finally, we can use the SAS (side-angle-side) Theorem to prove the triangles congruent (△ABC ≅ △CDA) because we have two sides and an angle between them that we know are congruent.