Question

is triangle bce congruent to triangle ade? explain your reasoning.

Explanation:

Step1: Identify vertical - angles

$\angle AED=\angle BEC$ because vertical angles are equal.

Step2: Identify given equal - sides

We are given that $AE = BE$ and $DE=CE$ (marked in the figure).

Step3: Apply SAS congruence criterion

In $\triangle ADE$ and $\triangle BCE$, we have $AE = BE$, $\angle AED=\angle BEC$, and $DE = CE$. By the Side - Angle - Side (SAS) congruence criterion, $\triangle ADE\cong\triangle BCE$.

Answer:

Yes, $\triangle BCE$ is congruent to $\triangle ADE$ by the SAS (Side - Angle - Side) congruence criterion.