Question

1.
2.
3.
4.

Explanation:

Step1: Analyze the given information for the first triangle pair

We are given \(\angle A\cong\angle C\), \(\angle E\cong\angle F\), and \(\overline{AE}\cong\overline{CF}\).
By the AAS (Angle - Angle - Side) congruence postulate, 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.
For \(\triangle AED\) and \(\triangle CFB\) (assuming the triangles formed by the given angles and side), since \(\angle A\cong\angle C\), \(\angle E\cong\angle F\), and \(\overline{AE}\cong\overline{CF}\), the congruence statement is \(\triangle AED\cong\triangle CFB\) by AAS.

Step2: Analyze the given information for the second triangle pair

We are given \(\overline{AF}\cong\overline{CF}\) and \(\overline{AE}\cong\overline{CE}\).
We only know two pairs of congruent sides. There is no information about the included angles or another pair of angles or sides.
By the SSS (Side - Side - Side) postulate, we need three pairs of congruent sides. By the SAS (Side - Angle - Side) postulate, we need two pairs of congruent sides and the included angle. Since we don't have enough information (no information about angles or the third side), we cannot prove the triangles \(\triangle AEF\) and \(\triangle CEF\) (assuming these are the triangles) congruent.

Answer:

1. \(\triangle AED\cong\triangle CFB\) by AAS.
2. Not possible. We only have two pairs of congruent sides (\(\overline{AF}\cong\overline{CF}\), \(\overline{AE}\cong\overline{CE}\)) and no information about angles or the third side to use SSS, SAS, ASA, or AAS.