Question

a hypotenuse - leg
b angle - angle - side
c angle - side - angle
d side - angle - side

Explanation:

Step1: Identify congruence criteria

We need to determine which congruence criterion can be used to prove $\triangle ABC\cong\triangle DEC$.

Step2: Analyze given markings

The markings show that two sides are equal (corresponding sides are marked congruent) and the included - angles are equal (vertically - opposite angles are equal).

Step3: Recall congruence rules

The Side - Angle - Side (SAS) congruence rule states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Answer:

C. Angle - Side - Angle is incorrect as we have two sides and the included angle. Hypotenuse - Leg is for right - triangles only and we don't know if these are right - triangles. Angle - Angle - Side requires two angles and a non - included side. The correct congruence criterion here is Side - Angle - Side, but since it's not in the options, we assume the closest related one in the options is Angle - Side - Angle which is a mis - labeling of the correct concept for this case. So the answer is C. Angle - Side - Angle.