Question

the proof that △acb≅△ecd is shown. given: ae and db bisect each other at c. prove: △acb≅△ecd. what is the missing statement in the proof? ∠acb≅∠ecd ∠bca≅∠dca ∠bac≅∠dec ∠acd≅∠ecb

Explanation:

Step1: Identify bisected segments

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

Step2: Recognize 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.

Answer:

$\angle ACB \cong \angle ECD$