QuestionProve the triangles below are congruent.
Given: $\angle B \cong \angle D, A C \cong C E$ Prove: $\triangle \mathrm{ACB} \cong \triangle \mathrm{ECD}$ 1) $\angle B \cong \angle D, A C \cong C E$ Given 2) $\angle A C B \cong \angle E C D$ [Choose] 3) $\triangle \mathrm{ACB} \cong \triangle E C D$ [Choose ]

Studdy Solution
Prove the congruence of the triangles using the ASA criterion:
2.1: Use the given information: - $\angle B \cong \angle D$ (Given) - $AC \cong CE$ (Given)
2.2: Identify the third angle: - Since $\angle ACB$ and $\angle ECD$ are vertical angles, they are congruent: $\angle ACB \cong \angle ECD$.
2.3: Apply the ASA criterion: - We have $\angle B \cong \angle D$, $AC \cong CE$, and $\angle ACB \cong \angle ECD$.
Therefore, by the ASA criterion, $\triangle ACB \cong \triangle ECD$.
The triangles $\triangle ACB$ and $\triangle ECD$ are congruent by the ASA criterion.