Question

determine if the triangles are congruent. if yes select the correct theorem. if no select not congruent
congruent select
theorem select

Explanation:

Step1: Identify equal sides

We have $AC = DC$ and $BC=EC$ as marked by the single and double - bar notations.

Step2: Identify the included angle

$\angle ACB$ and $\angle DCE$ are vertical angles. Vertical angles are equal, so $\angle ACB=\angle DCE$.

Step3: Apply congruence theorem

Since we have two pairs of equal sides and the included angles between them are equal, by the SAS (Side - Angle - Side) congruence theorem, $\triangle ABC\cong\triangle DEC$.

Answer:

Congruent: Yes
Theorem: SAS (Side - Angle - Side)