Question

are triangles abc and dec congruent? (1 point) yes, by sss yes, by aas yes, by sas not enough information

Explanation:

Step1: Identify vertical angles

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

Step2: Check given side - angle information

We know that $BC = EC$ (marked in the figure). Also, $\angle A=\angle D$ (given in the figure).

Step3: Apply AAS congruence criterion

The AAS (Angle - Angle - Side) congruence criterion states that if two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent. Here, in $\triangle ABC$ and $\triangle DEC$, we have $\angle A=\angle D$, $\angle ACB=\angle DCE$ (vertical angles), and $BC = EC$.

Answer:

Yes, by AAS.