Question

a side - side - side congruent triangle theorem b side - angle - sidcongruent triangle theorem c angle - angle - side congruent triangle theorem d angle - side - angle congruent triangle theorem e hypotenuse leg congruent triangle theorem f not congruent

Explanation:

Step1: Identify vertical angles

$\angle BCA$ and $\angle DCE$ are vertical angles. So, $\angle BCA=\angle DCE$.

Step2: Analyze side - angle - side

From the figure, $AC = EC$, $\angle BCA=\angle DCE$, and $BC = DC$. By the Side - Angle - Side (SAS) Congruent Triangle Theorem, $\triangle ABC\cong\triangle EDC$.

Answer:

B. Side - Angle - Side Congruent Triangle Theorem