This worksheet focuses on triangle congruence using the SAS (Side-Angle-Side) Congruence theorem. The specific problem presented involves proving that two triangles are congruent based on given information. Let's analyze the provided setup:

Given Information:

1. C is the midpoint (MP) of $\overline{AD}$ and $\overline{BE}$.
   • This means $AC = CD$ and $BC = CE$, which gives us two pairs of congruent sides.

The goal is to prove that $\triangle ABC \cong \triangle DEC$, most likely using the SAS Congruence Theorem.

Steps and reasons for the proof:

1. Statement: C is the midpoint of $\overline{AD}$ and $\overline{BE}$.

   • Reason: Given.

2. Statement: $\overline{AC} \cong \overline{CD}$ and $\overline{BC} \cong \overline{CE}$.

   • Reason: Definition of midpoint. Since C is the midpoint of both segments, these segments are congruent.

3. Statement: $\angle ACB \cong \angle DCE$.

   • Reason: Vertical angles are congruent. The two triangles share a pair of vertical angles formed by the intersecting lines.

4. Statement: $\triangle ABC \cong \triangle DEC$.

   • Reason: SAS Congruence Theorem. Two sides and the included angle are congruent.

Would you like further details on any of these steps or additional explanations?

Here are some related questions:

1. What is the difference between SAS and SSS congruence theorems?
2. How does the definition of a midpoint contribute to triangle congruence?
3. Why are vertical angles always congruent?
4. What are the key conditions to use the SAS Congruence Theorem?
5. How would the proof change if C was not the midpoint?

Tip: In triangle congruence proofs, always look for shared angles (like vertical angles) or common sides to simplify your reasoning.