https://file.aiquickdraw.com/mathbot/file/17289652570975144be92.jpg

Based on the flowchart and the triangle diagram you have uploaded, it looks like you're asked to complete a proof using a flowchart to show the congruence of two triangles.

### Observations:
- The diagram shows two right triangles, △ABD and △CBD, sharing a common side \( BD \) and having two equal angles at point B.
- The flowchart seems to require filling in reasons for the steps in a proof, leading to the conclusion that \( \triangle ABD \cong \triangle CBD \).

### Flowchart Breakdown:
1. **Given Information:**
   - "△ABD and △CBD are right triangles."
   - This is the given information, already filled in.

2. **Step 1: \( AB = CB \):**
   - Reason: This is likely due to the fact that these sides are equal, which could be due to the symmetry of the diagram.
   - The correct reason could be **"Given"** or **"Reflexive Property"** depending on what is previously stated.

3. **Step 2: \( BD = BD \):**
   - Reason: This is based on the fact that \( BD \) is a common side of both triangles.
   - The correct reason is **"Reflexive Property"**, since a side is congruent to itself.

4. **Conclusion: \( \triangle ABD \cong \triangle CBD \):**
   - Reason: Based on the information, the triangles are congruent by the **Hypotenuse-Leg (HL) Theorem**. This theorem applies when two right triangles have congruent hypotenuses and one leg in common.

### Complete Flowchart Proof:

1. **Given:**
   - △ABD and △CBD are right triangles. (Already given)
  
2. **\( AB = CB \):**
   - **Reason:** Given or Symmetry.

3. **\( BD = BD \):**
   - **Reason:** Reflexive Property.

4. **\( \triangle ABD \cong \triangle CBD \):**
   - **Reason:** Hypotenuse-Leg (HL) Theorem.

Would you like any further details or explanation on this? 

### Related Questions:
1. What is the Reflexive Property in geometry?
2. How does the Hypotenuse-Leg (HL) Theorem work in proving triangle congruence?
3. What other theorems could be used to prove triangle congruence?
4. Can the Symmetric Property be used in proving triangle congruence?
5. What are the other criteria for triangle congruence (like SSS, SAS, ASA)?

### Tip:
Always look for common sides or angles in triangles when trying to prove congruence—this simplifies the proof process.

Based on the given diagram, complete the flowchart proof below for triangle congruence.

Learn how to prove the congruence of two right triangles using a flowchart. This geometry problem involves the Hypotenuse-Leg (HL) Theorem and the Reflexive Property. Suitable for students in Grades 8-10.

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