Question

$\triangle pqr$ and $\triangle tsr$ are shown below.
which statement is true?
$\triangle pqr$ is similar to $\triangle tsr$.
$\triangle pqr$ is not similar to $\triangle tsr$.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Identify vertical angles

$\angle PRQ = \angle SRT$ (vertical angles are congruent)

Step2: Analyze side relationships

The arrows show $PQ \parallel ST$, so $\angle QPR = \angle STR$ and $\angle PQR = \angle TSR$ (alternate interior angles are congruent).

Step3: Apply similarity criterion

By AA (Angle-Angle) similarity, if two pairs of corresponding angles are congruent, the triangles are similar.

Answer:

$\triangle PQR$ is similar to $\triangle TSR$.