Question

$\triangle opq$ and $\triangle rpn$ are shown below.
which statement is true?
$\triangle opq$ is similar to $\triangle rpn$.
$\triangle opq$ is not similar to $\triangle rpn$.
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 equal angles

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

Step3: Apply AA similarity rule

Two pairs of corresponding angles are equal, so by AA (Angle-Angle) similarity criterion, the triangles are similar.

Answer:

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