Question

are the triangles congruent? why or why not? yes, they are congruent by either aas or asa. no, ∠c is not congruent to any angle in △def. no, the congruent sides do not correspond. yes, ∠a≅∠d and ab≅de.

Explanation:

Step1: Identify equal angles and sides

In $\triangle ABC$ and $\triangle DEF$, $\angle A = 33^{\circ}$, $\angle D=33^{\circ}$, and the marked - sides are equal. Also, we can find $\angle B=180^{\circ}-88^{\circ}-33^{\circ}=59^{\circ}$ and $\angle E = 58^{\circ}$, $\angle F=180^{\circ}-58^{\circ}-33^{\circ}=89^{\circ}$. But we know that $\angle A=\angle D = 33^{\circ}$, and the included side between the angles in both triangles are equal. Also, we can consider non - included side cases.

Step2: Apply congruence criteria

The Angle - Angle - Side (AAS) and Angle - Side - Angle (ASA) congruence criteria can be used. AAS states that 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, the triangles are congruent. ASA states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. Here we have the necessary angle and side equalities for either AAS or ASA.

Answer:

Yes, they are congruent by either AAS or ASA.