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: Identify triangle angles

In $\triangle CDE$: $\angle D = 90^\circ$, let $\angle C = \alpha$, so $\angle E = 90^\circ - \alpha$.
In $\triangle FGH$: $\angle G = 90^\circ$, the marked angles in $\triangle CDE$ match the non-right angles of $\triangle FGH$ (corresponding angles are equal).

Step2: Apply AA similarity rule

If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. Here, right angles are equal, and one pair of corresponding acute angles are equal, so AA similarity is satisfied.

Answer:

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