Congruent Triangles ADE and ABC: Analyzing Geometric Properties

Question

Triangles ADE and ABC are congruent.

Choose the correct answer.

00:00 Choose the appropriate answer

00:03 The triangles are similar according to the given data

00:09 According to the similarity ratio, we have pairs of corresponding sides

00:14 We take corresponding pairs of sides from each triangle

00:23 And this is the solution to the question

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.

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