https://file.aiquickdraw.com/mathbot/file/17265430275981hgmyg8v.jpg

Let's go through the flowchart and complete the proof based on the information provided in the image. Here's how we can complete each step:

1. **Given**: The problem states that *E is the midpoint of AC*.
   - Reason: **Given**

2. **AE ≅ EC**: Since E is the midpoint of AC, by definition, AE is congruent to EC.
   - Reason: **Definition of Midpoint**

3. **∠B ≅ ∠D**: These are **Vertical Angles**, and vertical angles are congruent.
   - Reason: **Vertical Angles Theorem**

4. **∠A ≅ ∠C**: These angles are also congruent due to **Alternate Interior Angles**, as AB and CD are intersected by the transversal line ED.
   - Reason: **Alternate Interior Angles Theorem**

5. **△ABE ≅ △CDE**: By the **ASA (Angle-Side-Angle) Congruence Postulate**, since we have two pairs of congruent angles (∠A ≅ ∠C and ∠B ≅ ∠D) and a congruent side (AE ≅ EC), the two triangles are congruent.
   - Reason: **ASA Postulate**

Would you like me to go over any specific parts of this proof or provide more details?

Here are 5 related questions that might help you expand your understanding:

1. What is the significance of the vertical angles theorem in proving congruence?
2. Can the triangles be proven congruent using a different congruence postulate like SAS (Side-Angle-Side)?
3. Why does the definition of a midpoint guarantee that two segments are congruent?
4. How does the alternate interior angles theorem apply when two lines are crossed by a transversal?
5. How would the proof change if E were not the midpoint of AC?

**Tip**: When solving triangle congruence proofs, always look for corresponding parts and theorems like ASA, SAS, or SSS to guide you through the steps.

Given E is the midpoint of AC, complete the flowchart proof below.

Solve the geometry problem involving triangle congruence proof with a flowchart, using the ASA postulate, midpoint definitions, and angle congruence theorems. This is ideal for students in Grades 9-10 learning about congruent triangles and geometric proofs.

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