https://file.aiquickdraw.com/mathbot/file/17302104238985btgz56d.jpg

To find the value of \( BD \) in this diagram, let's analyze the information provided:

1. **Congruent Triangles**: The problem states that \( \triangle ABC \) is congruent to \( \triangle DBC \). This means all corresponding sides and angles of these triangles are equal.

2. **Side Lengths**: We have:
   - \( AB = AC = 4 \) inches.
   - \( BC = 5 \) inches.

3. **Side \( BD \)**: Since \( \triangle ABC \) and \( \triangle DBC \) are congruent, side \( BD \) is equal to side \( AB \) or \( AC \).

Therefore:
\[
BD = 4 \text{ inches}
\]

So, the correct answer is:
- **4 inches**

Do you want further explanation on congruent triangles, or have any other questions?

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Here are five related questions to deepen understanding:
1. What are the criteria for two triangles to be congruent?
2. How do you find the length of a side in congruent triangles?
3. Can congruent triangles have different angles?
4. If \( BC \) were not equal in both

Triangle ABC is congruent to Triangle DBC. Given that AB = 4 in, AC = 4 in, and BC = 5 in, find the length of BD.

Understand how to find the side length BD in congruent triangles ABC and DBC with given side lengths AB = 4 in and BC = 5 in. Learn key concepts in geometry, including triangle congruence.

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