Question

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

Explanation:

Step1: Calculate the third angle of $\triangle FGH$

The sum of angles in a triangle is $180^{\circ}$. In $\triangle FGH$, we know two angles: $\angle G = 90^{\circ}$ and $\angle F=50^{\circ}$. Let $\angle H = x$. Then $x + 90^{\circ}+50^{\circ}=180^{\circ}$, so $x=180^{\circ}-(90^{\circ} + 50^{\circ})=40^{\circ}$.

Step2: Check for angle - angle similarity

In $\triangle CDE$, $\angle D = 90^{\circ}$. In $\triangle FGH$, $\angle G = 90^{\circ}$. Also, if we assume that the non - right angles can be compared (by the angle - angle similarity criterion which states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar). Since we have two right - angled triangles and we can match the angles (the remaining angles in the right - angled triangles can be compared based on the angle sum property of triangles).

Answer:

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