The diagram presents two overlapping triangles, $\triangle ABC$ and $\triangle DEC$, with the goal of proving that $AC \cong DC$ using the given information:

Given Information:

1. $\angle ABC \cong \angle DEC$ (corresponding angles are congruent)
2. $BC \cong EC$ (corresponding sides are congruent)

Proof Plan:

We aim to show that $AC \cong DC$ by using the Side-Angle-Side (SAS) congruence postulate, which states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent.

Proof Steps:

1. Statement: $\angle ABC \cong \angle DEC$
   • Reason: Given
2. Statement: $BC \cong EC$
   • Reason: Given
3. Statement: $AC \cong DC$
   • Reason: Triangles $\triangle ABC$ and $\triangle DEC$ are congruent by the SAS postulate, since two sides and the included angle are congruent.

This completes the proof.

Do you want more details or have any questions?

Related Questions:

1. What is the SAS (Side-Angle-Side) postulate in geometry?
2. How can we prove two triangles are congruent using the ASA postulate?
3. What are some common mistakes when proving triangles congruent?
4. How can corresponding parts of congruent triangles be proven equal?
5. How do alternate interior angles relate to triangle congruence?

Tip: When proving triangles congruent, always identify the corresponding sides and angles correctly to avoid confusion.