Question

the proof that $\triangle acb \cong \triangle ecd$ is shown. given: $\overline{ae}$ and $\overline{db}$ bisect each other at $c$. prove: $\triangle acb \cong \triangle ecd$ what is the missing statement in the proof? $\bigcirc \angle bac \cong \angle dec$ $\bigcirc \angle acd \cong \angle ecb$ $\bigcirc \angle acb \cong \angle ecd$ $\bigcirc \angle bca \cong \angle dca$

Explanation:

Step1: Identify given condition

$\overline{AE}$ and $\overline{DB}$ bisect each other at $C$, so $AC=EC$ and $BC=DC$.

Step2: Identify vertical angles

$\angle ACB$ and $\angle ECD$ are vertical angles, so $\angle ACB \cong \angle ECD$.

Step3: Apply SAS congruence

With $AC=EC$, $\angle ACB \cong \angle ECD$, $BC=DC$, $\triangle ACB \cong \triangle ECD$ by SAS. The missing statement is $\angle ACB \cong \angle ECD$.

Answer:

B. $\angle ACB \cong \angle ECD$