Question

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

Explanation:

Step1: Find the measure of $\angle C$

In $\triangle CDE$, $\angle D = 90^{\circ}$ and $\angle DEC=46^{\circ}$. Using the angle - sum property of a triangle ($\angle C+\angle D+\angle DEC = 180^{\circ}$), we get $\angle C=180^{\circ}-\angle D - \angle DEC$. Substituting the values, $\angle C=180^{\circ}-90^{\circ}-46^{\circ}=44^{\circ}$.

Step2: Check the similarity of triangles

In $\triangle CDE$ and $\triangle FGE$, $\angle C = 44^{\circ}$ and $\angle F = 44^{\circ}$, $\angle D=\angle G = 90^{\circ}$. By the AA (Angle - Angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar), since two pairs of corresponding angles are equal, $\triangle CDE\sim\triangle FGE$.

Answer:

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