1. **Problem Statement:** We need to determine which additional information is sufficient to prove that triangle $ABC$ is congruent to triangle $EBD$ given that lines $m$ and $n$ are parallel and line segments $AE$ and $CD$ intersect at point $B$. 2. **Given:** - Lines $m \parallel n$. - $AE$ and $CD$ intersect at $B$. 3. **Goal:** Prove $\triangle ABC \cong \triangle EBD$. 4. **Key Congruence Criteria:** Triangles are congruent if they satisfy one of the following: - Side-Angle-Side (SAS) - Angle-Side-Angle (ASA) - Side-Side-Side (SSS) - Angle-Angle-Side (AAS) 5. **Analysis:** - Since $m \parallel n$, alternate interior angles formed by transversal $AE$ and $CD$ are equal. - $\angle ABC = \angle EBD$ because they are vertical angles. 6. **Check each option:** **a.** $AB = 16$ and $DB = 16$. - Sides $AB$ and $DB$ are equal. - We have $\angle ABC = \angle EBD$ (vertical angles). - Also, $\angle BAC = \angle BDE$ (alternate interior angles due to parallel lines). - This gives us SAS congruence. **b.** $AB = 16$ and $EB = 16$. - Sides $AB$ and $EB$ are equal but they are not corresponding sides in the triangles. - This does not guarantee congruence. **c.** Triangles $ABC$ and $EBD$ are isosceles. - Being isosceles alone does not guarantee congruence. **d.** No additional information is necessary. - Without additional side length information, congruence cannot be established. 7. **Conclusion:** Option (a) provides sufficient information to prove $\triangle ABC \cong \triangle EBD$ by SAS. **Final answer:** a. $AB = 16$ and $DB = 16$