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.

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.

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!