Similar Triangles: Analyzing the Relationship Between Triangle EDB and ABC

The key property of similar triangles is that the ratios of the lengths of their corresponding sides are equal. For triangles EDB and ABC:

• Triangle EDB is similar to triangle ABC, meaning:
• Corresponding sides are proportional: $\frac{AB}{BE} = \frac{BC}{DB} = \frac{AC}{ED}$

Therefore, the correct relationship among the sides, using the concept of similar triangles, is:

$\frac{BC}{DB} = \frac{AB}{BE} = \frac{AC}{ED}$

This matches choice 3.

Thus, the correct answer to the problem is $\frac{BC}{DB}=\frac{AB}{BE}=\frac{AC}{ED}$.