Question

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

Explanation:

Step1: Check vertical angles

$\angle PRQ=\angle SRT$ (vertical angles are equal).

Step2: Check parallel - line - related angles

Since the sides with the red arrows (assuming they are parallel), by the alternate - interior angles theorem, $\angle Q=\angle T$.

Step3: Use AA (Angle - Angle) similarity criterion

In $\triangle PQR$ and $\triangle TSR$, we have two pairs of equal angles ($\angle Q=\angle T$ and $\angle PRQ=\angle SRT$). By the AA similarity criterion, if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

Answer:

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