We are given that $D$ is the midpoint of $\overline{AC}$, $\angle AED \cong \angle CFD$, and $\angle EDA \cong \angle FDC$. We want to prove that $\triangle AED \cong \triangle CFD$.

1. Problem Description

We are given that $D$ is the midpoint of $\overline{AC}$, $\angle AED \cong \angle CFD$, and $\angle EDA \cong \angle FDC$. We want to prove that $\triangle AED \cong \triangle CFD$.

2. Solution Steps

We are given that $D$ is the midpoint of $\overline{AC}$. This implies that $AD = CD$ by the definition of a midpoint.

We are also given that $\angle AED \cong \angle CFD$ and $\angle EDA \cong \angle FDC$.

Therefore, we have two angles and a non-included side congruent. Since we have two angles and the non-included side (AAS theorem) we can show that the triangles are congruent.

Statement | Reason

------- | --------

1. $D$ is the midpoint of $\overline{AC}$, $\angle AED \cong \angle CFD$, $\angle EDA \cong \angle FDC$ | Given

2. $AD = CD$ | Definition of midpoint

3. $\triangle AED \cong \triangle CFD$ | Angle-Angle-Side (AAS) Theorem

3. Final Answer

$\triangle AED \cong \triangle CFD$