1. **State the problem:** Prove that \(\triangle GED \cong \triangle GFD\) given that both are right triangles and \(\overline{DE} \cong \overline{DF}\). 2. **Given:** - \(\triangle GED\) and \(\triangle GFD\) are right triangles. - \(\overline{DE} \cong \overline{DF}\). 3. **Identify the shared side:** Both triangles share side \(\overline{GD}\). 4. **Use the RHS (Right angle-Hypotenuse-Side) congruence theorem:** - Both triangles have a right angle (given). - The hypotenuses \(\overline{DE}\) and \(\overline{DF}\) are congruent (given). - The side \(\overline{GD}\) is common to both triangles. 5. **Conclusion:** By the RHS congruence theorem, \(\triangle GED \cong \triangle GFD\). This completes the proof.