Question

△def and △jkl are shown below.
which statement is true?
△def is similar to △jkl.
△def is not similar to △jkl.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Find the third angle of $\triangle DEF$

In a right - angled triangle, the sum of angles is $180^{\circ}$. For $\triangle DEF$ with $\angle E = 90^{\circ}$ and $\angle F=32^{\circ}$, we use the formula $\angle D=180^{\circ}-\angle E - \angle F$.
So, $\angle D=180^{\circ}-90^{\circ}-32^{\circ}=58^{\circ}$.

Step2: Find the third angle of $\triangle JKL$

For $\triangle JKL$ with $\angle K = 90^{\circ}$ and $\angle J = 52^{\circ}$, using the formula $\angle L=180^{\circ}-\angle K-\angle J$.
So, $\angle L=180^{\circ}-90^{\circ}-52^{\circ}=38^{\circ}$.

Step3: Check the similarity condition

Two triangles are similar if their corresponding angles are equal. Since the angles of $\triangle DEF$ ($90^{\circ},32^{\circ},58^{\circ}$) and $\triangle JKL$ ($90^{\circ},52^{\circ},38^{\circ}$) are not equal.

Answer:

$\triangle DEF$ is not similar to $\triangle JKL$.