Congruent Triangles ADE and ABC: Analyzing Geometric Properties

To find the correct proportionality relationship between the triangles ADE and ABC, we need to identify the corresponding sides:

• In triangle ADE, the sides $AD$, $AE$, and $DE$ correspond to triangle ABC’s sides $AB$, $AC$, and $BC$, respectively.

Because these triangles are congruent, the ratios of their corresponding sides are equal:

$\frac{AD}{AB} = \frac{AE}{AC} = \frac{DE}{BC}$

This relationship matches with choice 1:

$\frac{AD}{AB}=\frac{AE}{AC}=\frac{DE}{BC}$

Therefore, the correct answer is choice 1.