Question

$\triangle abc$ and $\triangle dec$ are shown below.

which statement is true?
$\triangle abc$ is similar to $\triangle dec$.
$\triangle abc$ is not similar to $\triangle dec$.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Identify given congruent sides

From the diagram:
$AB \cong BC$ (single tick marks), so $\triangle ABC$ is an isosceles right triangle, with $\frac{AB}{BC}=1$.
$CE \cong DE$ (double tick marks), so $\triangle DEC$ is an isosceles right triangle, with $\frac{DE}{CE}=1$.

Step2: Verify right angles

$\angle B = \angle E = 90^\circ$ (marked right angles).

Step3: Check side ratio similarity

For right triangles, if the ratio of corresponding legs is equal, the triangles are similar by SAS similarity.
Corresponding leg ratios:
$\frac{AB}{DE} = \frac{BC}{CE}$ (since $\frac{AB}{BC}=1$ and $\frac{DE}{CE}=1$, so $\frac{AB}{DE}=\frac{BC}{CE}$).
Also, the included angles (the right angles) are congruent.

Answer:

$\triangle ABC$ is similar to $\triangle DEC$.