To analyze and solve this problem, let's go through the details visible in the image.

1. Determine if the triangles are congruent: We have two triangles, $\triangle CDE$ and $\triangle FGH$, which need to be checked for congruency.

2. Identify the method for congruency:

   • From the diagram, we can see that:
     • Segment $\overline{CE}$ is marked congruent to $\overline{FG}$.
     • Angle $\angle DCE$ is marked congruent to $\angle HFG$.
     • Segment $\overline{DE}$ is marked congruent to $\overline{GH}$.
   • Based on these congruent parts (two sides and the included angle), we can use the SAS (Side-Angle-Side) postulate to prove the triangles are congruent.

3. Complete the congruency statement:

   • The congruent parts can be listed as:
     • $\overline{CE} \cong \overline{FG}$
     • $\overline{DE} \cong \overline{GH}$
     • $\angle DCE \cong \angle HFG$
   • Therefore, we can conclude $\triangle CDE \cong \triangle FGH$ by the SAS Postulate.

4. Identify the transformation: Since the triangles appear to be mirror images across the line between points $E$ and $F$, the transformation that maps $\triangle CDE$ onto $\triangle FGH$ is a Reflection.

Final Answers:

• Are the triangles congruent? Yes
• Method used: SAS
• Congruent parts:
  • $\overline{CE} \cong \overline{FG}$
  • $\overline{DE} \cong \overline{GH}$
  • $\angle DCE \cong \angle HFG$
• Congruence statement: $\triangle CDE \cong \triangle FGH$
• Transformation: Reflection

Would you like more detailed explanations on each step or have any questions?

Here are five related questions that might expand on this content:

1. What are the other triangle congruence postulates besides SAS, and when are they used?
2. How can you determine if a transformation is a rotation, reflection, or translation based on a figure?
3. Can triangles still be congruent if only two sides and a non-included angle are known to be equal?
4. How would the answer change if the marked angles were not included between the two congruent sides?
5. In which situations would a translation be the correct transformation for congruent figures?

Tip: Always verify the location of the angle in congruency statements; the included angle is essential for the SAS postulate.