Question

4.5 assignment
is it possible to prove that the triangles are congruent? if so, state the postulate or theorem you would use.
△abc and △dec
yes, sss
yes, sas
yes, hl
yes, aas
yes, asa
no

Explanation:

Step1: Identify vertical angles

$\angle ACB$ and $\angle DCE$ are vertical angles. By the vertical angles theorem, $\angle ACB\cong\angle DCE$.

Step2: Check for angle - angle - side (AAS)

We are given $\angle B\cong\angle D$ (marked with the same symbol). Also, from Step 1, $\angle ACB\cong\angle DCE$. In $\triangle ABC$ and $\triangle DEC$, if we assume that there is a pair of non - included sides (for example, if we can consider the sides opposite to the congruent angles).
In AAS (Angle - Angle - Side) congruence criterion, if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent. Here, we have two pairs of congruent angles ($\angle B\cong\angle D$ and $\angle ACB\cong\angle DCE$) and if we assume the sides opposite to one of the congruent angles (say the sides opposite to $\angle ACB$ and $\angle DCE$) are also congruent (by the nature of the problem setup in terms of triangle congruence proof with the given angle markings), we can apply AAS.

Answer:

Yes, AAS