Congruent Triangles ADE and ABC: Geometric Properties Analysis

Triangles ADE and ABC are given as congruent. When two triangles are congruent, their corresponding sides are equal in proportion. Therefore, we need to find the correct proportional relationship between the sides of these triangles.

Let's recall that for two congruent triangles, their corresponding sides are in equal ratios. Specifically, for triangles ADE and ABC, the sides AD, AE, and DE correspond to the sides AB, AC, and BC, respectively.

Thus, the correct proportional relationship between the corresponding sides of triangles ADE and ABC is:

• $\frac{AD}{AB}$ corresponding to the first set of sides.
• $\frac{AE}{AC}$ corresponding to the second set of sides.
• $\frac{DE}{BC}$ corresponding to the third set of sides.

Therefore, the choice that correctly represents the proportional relationship of the sides of triangles ADE and ABC is:

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