Question

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

Explanation:

Step1: Identify shared angle

$\angle P$ is common to $\triangle OPQ$ and $\triangle RPN$.

Step2: Identify given equal angles

$\angle POQ = \angle PRN$ (marked congruent angles).

Step3: Apply AA similarity criterion

If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. Here, $\angle P \cong \angle P$ and $\angle POQ \cong \angle PRN$, so $\triangle OPQ \sim \triangle RPN$.

Answer:

$\triangle OPQ$ is similar to $\triangle RPN$.