Question

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

Explanation:

Step1: Find angle in $\triangle CDE$

In $\triangle CDE$, since $\angle D = 90^{\circ}$, and the sum of angles in a triangle is $180^{\circ}$. Let's find $\angle C$.
$\angle C=180^{\circ}-\angle D - \angle E$. We assume $\angle E$ is the non - right angle. But we can also use the fact that we can compare with the other triangle's angles. In $\triangle FGH$, $\angle G = 90^{\circ}$, $\angle F=50^{\circ}$, then $\angle H=180^{\circ}-\angle G-\angle F=180^{\circ}- 90^{\circ}-50^{\circ}=40^{\circ}$.
In $\triangle CDE$, assume the non - right angles are complementary to the right angle. If we consider the angle - angle (AA) similarity criterion.
We know that in $\triangle CDE$ and $\triangle FGH$, $\angle D=\angle G = 90^{\circ}$ and $\angle H = 40^{\circ}$, assume the non - right angle in $\triangle CDE$ corresponding to $\angle H$ is also $40^{\circ}$ (since the non - right angles in right - angled triangles are complementary to the right angle).
Since two angles of $\triangle CDE$ are equal to two angles of $\triangle FGH$ ( $\angle D=\angle G$ and one of the non - right angles are equal), by the AA (angle - angle) similarity criterion for triangles.

Step2: Apply similarity criterion

By the AA similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the two triangles are similar.
So, $\triangle CDE\sim\triangle FGH$.

Answer:

$\triangle CDE$ is similar to $\triangle FGH$.