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Thank you for uploading the image. I see a problem involving a **triangle congruence flowchart proof** related to the angle bisector \( BD \) in \( \triangle ABC \). Let's walk through how to complete this proof based on what’s visible.

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### Step-by-Step Reasoning:

1. **Given:**
   - \( BD \) is the angle bisector of \( \angle ABC \). This is the **starting point** of the proof.

2. **Next Steps in the Flowchart:**
   - **Angle \( \angle ABD \cong \angle CBD \):**  
     **Reason:** *Definition of angle bisector*  
     - Since \( BD \) bisects \( \angle ABC \), the two smaller angles \( \angle ABD \) and \( \angle CBD \) are congruent.

   - **Side \( BD \cong BD \):**  
     **Reason:** *Reflexive Property*  
     - A segment is always congruent to itself, so \( BD \cong BD \).

   - **Angle \( \angle A \cong \angle C \):**  
     **Reason:** *Given* (or could be marked as a shared property, depending on what’s known about the problem).

3. **Final Congruence:**
   - \( \triangle ABD \cong \triangle CBD \)  
     **Reason:** *ASA (Angle-Side-Angle) Congruence Criterion*  
     - We now have two pairs of corresponding angles congruent (the bisected angles and possibly \( \angle A \cong \angle C \)) and the included side \( BD \) congruent by the reflexive property.

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Does this solve your question?  
Here are some **related questions** for further practice:

1. How does the reflexive property help in proving congruence?
2. What are the different triangle congruence criteria (e.g., SSS, SAS, ASA, AAS, HL)?
3. How does an angle bisector divide a triangle?
4. Can two triangles be congruent if only two angles are congruent?
5. What is the difference between congruence and similarity in triangles?

**Tip:** Always look for congruent angles or sides marked in diagrams when working with proofs!

Given BD is the angle bisector of ∠ABC, complete the flowchart proof to show that △ABD ≅ △CBD.

Learn how to complete a triangle congruence flowchart proof involving △ABD and △CBD. This problem explores geometry concepts such as the angle bisector, ASA congruence criterion, and reflexive property, suitable for Grades 9-10.

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